Edit Profile (opens in new tab) Kolokoltsov, Vassili N. Compute Distance To: Compute Author ID: kolokoltsov.vassili-n Published as: Kolokoltsov, Vassili N.; Kolokol’tsov, V. N.; Kolokoltsov, V. N.; Kolokoltsov, Vassili; Kolokol’tsov, Vassili N.; Kolokoltsov, V.; Kolokoltsov, Vassily; Kolokol’tsov, Vassiliĭ N.; Kolokoltsov, Vassily N. more...less Documents Indexed: 128 Publications since 1982, including 10 Books 1 Contribution as Editor Co-Authors: 70 Co-Authors with 67 Joint Publications 2,503 Co-Co-Authors all top 5 Co-Authors 58 single-authored 11 Maslov, Viktor Pavlovich 7 Albeverio, Sergio A. 6 Dobrokhotov, Sergei Yurievich 6 Troeva, Marianna S. 5 Hilbert, Astrid 5 Malafeev, Oleg Alekseivich 4 Hernández-Hernández, Ma. Elena 4 Korolev, Viktor Yur’evich 3 Akian, Marianne 3 Bening, Vladimir E. 3 Binner, Jane M. 3 Ciardiello, Francesco 3 Fletcher, Leslie R. 3 Gaubert, Stéphane 3 Uchaĭkin, Vladimir Vasil’evich 3 Veretennikova, Maria A. 2 Belavkin, Viacheslav 2 Saenko, Viacheslav V. 2 Schilling, René Leander 2 Smolyanov, Oleg Georgievich 1 Ageev, Oleg N. 1 Aubin, Jean-Pierre 1 Ball, Robin C. 1 Basna, Rani 1 Bensoussan, Alain 1 Bernhard, Pierre 1 Cecchin, Alekos 1 Del Moral, Pierre 1 Efremova, Lyudmila S. 1 Engwerda, Jacob Christiaan 1 Gorban, Alexander N. 1 Grigorchuk, Rostislav Ivanovich 1 Grines, Vyacheslav Zigmundovich 1 Gurevich, B. M. 1 Gusarov, G. G. 1 Helemskii, Alexander Ya. 1 Hucki, Z. 1 Kashin, Boris Sergeevich 1 Katsikas, Stamatios 1 Kochergin, Andrey V. 1 Lee, Rui Xin 1 Lerman, Lev 1 Lin, Feng 1 MacKay, Robert Sinclair 1 Makarov, Konstantin A. 1 Martines Olive, Victor 1 Mijatović, Aleksandar 1 Mykytyuk, Ihor V. 1 Olivé, Victor M. 1 Oseledets, Valeriĭ Iustinovich 1 Plakhov, A. Yu 1 Pochinka, Olga Vital’evna 1 Roorda, Berend 1 Ryzkhikov, V. V. 1 Saint-Pierre, Patrick 1 Sakbaev, Vsevolod Zhanovich 1 Schumacher, Johannes M. 1 Sergeev, Armen Glebovich 1 Shafarevich, Andreĭ Igorevich 1 Sinaĭ, Yakov Grigor’evich 1 Sukhorukova, T. A. 1 Tagi-Zade, A. T. 1 Thouvenot, Jean-Paul 1 Toniazzi, Lorenzo 1 Tyukov, Alexei E. 1 Tyukov, Alexey E. 1 Vorobets, Ya. B. 1 Weiss, Benjamin 1 Zhirov, Aleksei Yu 1 Zhuzhoma, Evgeniĭ Viktorovich 1 Zolotarëv, Vladimir Mikhaĭlovich all top 5 Serials 4 Mathematical Notes 4 Stochastics and Stochastics Reports 4 Journal of Mathematical Sciences (New York) 4 Fractional Calculus & Applied Analysis 4 Dynamic Games and Applications 3 Theoretical and Mathematical Physics 3 Soviet Mathematics. Doklady 3 Probability Theory and Related Fields 3 Russian Academy of Sciences. Doklady. Mathematics 3 Stochastics 3 Games 2 Journal of Mathematical Physics 2 Journal of Statistical Physics 2 Matematicheskie Zametki 2 Russian Mathematical Surveys 2 Reviews in Mathematical Physics 2 Applied Mathematics and Optimization 2 Functional Analysis and its Applications 2 Stochastic Analysis and Applications 2 Russian Journal of Mathematical Physics 2 Electronic Journal of Probability 2 Markov Processes and Related Fields 2 International Game Theory Review 2 Proceedings of the Steklov Institute of Mathematics 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Moscow University Mathematics Bulletin 1 Chaos, Solitons and Fractals 1 Theory of Probability and its Applications 1 Funktsional’nyĭ Analiz i ego Prilozheniya 1 International Journal of Game Theory 1 Journal of Applied Probability 1 Kybernetika 1 Mathematics of Operations Research 1 Mathematics of the USSR. Izvestiya 1 Proceedings of the London Mathematical Society. Third Series 1 Transactions of the Moscow Mathematical Society 1 Comptes Rendus Mathématiques de l’Académie des Sciences 1 Revista Matemática Iberoamericana 1 Journal of Theoretical Probability 1 The Annals of Applied Probability 1 Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya 1 Stochastic Processes and their Applications 1 Comptes Rendus de l’Académie des Sciences. Série I 1 Potential Analysis 1 Electronic Journal of Differential Equations (EJDE) 1 Filomat 1 Sbornik: Mathematics 1 Infinite Dimensional Analysis, Quantum Probability and Related Topics 1 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Journal of Dynamical and Control Systems 1 Methodology and Computing in Applied Probability 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Advanced Studies in Contemporary Mathematics (Kyungshang) 1 Cambridge Tracts in Mathematics 1 De Gruyter Studies in Mathematics 1 Lecture Notes in Mathematics 1 London Mathematical Society Lecture Note Series 1 Mathematics and its Applications (Dordrecht) 1 Mathematical Modelling of Natural Phenomena 1 Risk and Decision Analysis 1 Matematicheskaya Teoriya Igr i eë Prilozheniya 1 Communications in Applied and Industrial Mathematics 1 Journal of Fractional Calculus and Applications 1 Fractional Differential Calculus 1 Problemy Analiza. Issues of Analysis 1 Journal of Applied Nonlinear Dynamics 1 Springer Series in Operations Research and Financial Engineering 1 Static & Dynamic Game Theory: Foundations & Applications 1 Birkhäuser Advanced Texts. Basler Lehrbücher all top 5 Fields 61 Probability theory and stochastic processes (60-XX) 36 Partial differential equations (35-XX) 32 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 25 Quantum theory (81-XX) 22 Calculus of variations and optimal control; optimization (49-XX) 15 Statistical mechanics, structure of matter (82-XX) 11 Operator theory (47-XX) 11 Operations research, mathematical programming (90-XX) 8 Ordinary differential equations (34-XX) 7 Real functions (26-XX) 7 Global analysis, analysis on manifolds (58-XX) 7 Systems theory; control (93-XX) 6 Dynamical systems and ergodic theory (37-XX) 5 Differential geometry (53-XX) 5 Mechanics of particles and systems (70-XX) 4 Functional analysis (46-XX) 2 Order, lattices, ordered algebraic structures (06-XX) 2 Special functions (33-XX) 2 Integral transforms, operational calculus (44-XX) 2 Statistics (62-XX) 2 Fluid mechanics (76-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Associative rings and algebras (16-XX) 1 Group theory and generalizations (20-XX) 1 Measure and integration (28-XX) 1 Difference and functional equations (39-XX) 1 Approximations and expansions (41-XX) 1 Integral equations (45-XX) 1 Numerical analysis (65-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Information and communication theory, circuits (94-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 100 Publications have been cited 924 times in 673 Documents Cited by ▼ Year ▼ Idempotent analysis and its applications. Appendix by Pierre Del Moral. Transl. from the Russian by V. E. Nazaikinskij. Zbl 0941.93001Kolokoltsov, V. N.; Maslov, V. P. 118 1997 Symmetric stable laws and stable-like jump-diffusions. Zbl 1021.60011Kolokoltsov, Vassili 100 2000 Markov processes, semigroups and generators. Zbl 1220.60003Kolokoltsov, Vassili N. 70 2011 Nonlinear Markov processes and kinetic equations. Zbl 1222.60003Kolokoltsov, Vassili N. 67 2010 Semiclassical analysis for diffusions and stochastic processes. Zbl 0951.60001Kolokoltsov, V. N. 37 2000 Generalized continuous-time random walks, subordination by hitting times, and fractional dynamics. Zbl 1193.60046Kolokoltsov, V. N. 33 2009 Geodesic flows on two-dimensional manifolds with an additional first integral that is polynomial in the velocities. Zbl 0548.58028Kolokol’tsov, V. N. 20 1983 On the rate of convergence for the mean-field approximation of controlled diffusions with large number of players. Zbl 1314.91020Kolokoltsov, Vassili N.; Troeva, Marianna; Yang, Wei 18 2014 On fully mixed and multidimensional extensions of the Caputo and Riemann-Liouville derivatives, related Markov processes and fractional differential equations. Zbl 1321.26013Kolokoltsov, Vassili 18 2015 Nonexpansive maps and option pricing theory. Zbl 1274.91420Kolokoltsov, Vassili N. 17 1998 Generalised fractional evolution equations of Caputo type. Zbl 1374.34009Hernández-Hernández, M. E.; Kolokoltsov, V. N.; Toniazzi, L. 15 2017 Idempotent analysis as a tool of control theory and optimal synthesis. I. Zbl 0709.49014Kolokol’tsov, V. N.; Maslov, V. P. 14 1989 On mean field games with common noise and McKean-Vlasov SPDEs. Zbl 1415.60075Kolokoltsov, Vassili N.; Troeva, Marianna 13 2019 Well-posedness and regularity of the Cauchy problem for nonlinear fractional in time and space equations. Zbl 1412.35370Kolokoltsov, V. N.; Veretennikova, M. A. 13 2014 A fractional Hamilton Jacobi Bellman equation for scaled limits of controlled continuous time random walks. Zbl 1329.60117Kolokoltsov, Vassili N.; Veretennikova, Maria A. 12 2014 The interval market model in mathematical finance. Game-theoretic methods. Zbl 1279.91005Bernhard, Pierre; Engwerda, Jacob C.; Roorda, Berend; Schumacher, Johannes M.; Kolokoltsov, Vassili; Saint-Pierre, Patrick; Aubin, Jean-Pierre 12 2013 Turnpike theorems for Markov games. Zbl 1272.91027Kolokoltsov, Vassili; Yang, Wei 12 2012 Splitting of the lowest energy levels of the Schrödinger equation and asymptotic behavior of the fundamental solution of the equation \(hu_ t=h^ 2\Delta u/2-V(x)u\). Zbl 0745.35033Dobrokhotov, S. Yu.; Kolokol’tsov, V. N.; Maslov, V. P. 11 1991 Mean-field-game model of corruption. Zbl 1391.91030Kolokoltsov, V. N.; Malafeyev, O. A. 11 2017 Geodesic flows on two-dimensional manifolds with according to the velocities complementary polynomial first integral. Zbl 0518.58033Kolokol’tsov, V. N. 11 1982 On linear, additive, and homogeneous operators in idempotent analysis. Zbl 0925.47016Kolokoltsov, V. N. 10 1992 Set coverings and invertibility of functional Galois connections. Zbl 1080.06001Akian, Marianne; Gaubert, Stéphane; Kolokoltsov, Vassili 10 2005 On Markov processes with decomposable pseudo-differential generators. Zbl 1091.60014Kolokoltsov, Vassili N. 10 2004 Asymptotic spectral analysis of a small diffusion operator and the life times of the corresponding diffusion process. Zbl 0912.58042Kolokol’tsov, Vassili N.; Makarov, Konstantin A. 10 1996 Scattering theory for the Belavkin equation describing a quantum particle with continuously observed coordinate. Zbl 0845.35078Kolokol’tsov, Vassili N. 10 1995 The probabilistic point of view on the generalized fractional partial differential equations. Zbl 1483.35002Kolokoltsov, Vassili N. 10 2019 Many agent games in socio-economic systems: corruption, inspection, coalition building, network growth, security. Zbl 1431.91004Kolokoltsov, Vassili N.; Malafeyev, Oleg A. 10 2019 Nonlinear Markov semigroups and interacting Lévy type processes. Zbl 1110.82029Kolokoltsov, Vassili N. 9 2007 Fractional stable distributions. Zbl 0994.60010Kolokoltsov, V.; Korolev, V.; Uchaikin, V. 8 2001 Mean-field-game model for botnet defense in cyber-security. Zbl 1372.49049Kolokoltsov, V. N.; Bensoussan, A. 8 2016 Differential equations on measures and functional spaces. Zbl 1451.34001Kolokoltsov, Vassili 8 2019 Splitting amplitudes of the lowest energy levels of the Schrödinger operator with double-well potential. Zbl 0799.35050Dobrokhotov, S. Yu.; Kolokol’tsov, V. N. 7 1993 Invertibility of functional Galois connections. Zbl 1022.06001Akian, Marianne; Gaubert, Stéphane; Kolokoltsov, Vassili 7 2002 Idempotent analysis and its applications to optimal control. (Idempotentnyj analiz i ego primenenie v optimal’nom upravlenii.) Zbl 0857.49022Maslov, V. P.; Kolokol’tsov, V. N. 7 1994 The evolutionary game of pressure (or interference), resistance and collaboration. Zbl 1386.91028Kolokoltsov, Vassili 7 2017 Continuous quantum measurement: Local and global approaches. Zbl 0894.47058Albeverio, S.; Kolokol’tsov, V. N.; Smolyanov, O. G. 6 1997 Stochastic duality of Markov processes: A study via generators. Zbl 1291.60154Kolokoltsov, Vassili; Lee, Rui Xin 6 2013 The double-well splitting of the low energy levels for the Schrödinger operator of discrete \(\varphi^ 4\)-models on tori. Zbl 0820.60097Dobrokhotov, Sergei Yu.; Kolokol’tsov, Vassili N. 6 1995 Localization and analytic properties of the solutions of the simplest quantum filtering equation. Zbl 0927.60088Kolokol’tsov, Vassili N. 6 1998 Estimation of parameters of fractional stable distributions. Zbl 1130.62023Bening, V. E.; Korolev, V. Yu.; Kolokol’tsov, V. N.; Saenko, V. V.; Uchaikin, V. V.; Zolotarev, V. M. 5 2004 Estimates uniform in time for the transition probability of diffusions with small drift and for stochastically perturbed Newton equations. Zbl 0928.60061Albeverio, Sergio; Hilbert, Astrid; Kolokoltsov, Vassili 5 1999 The general form of the endomorphisms in the space of continuous functions with values in a numerical commutative semiring (with the operation \(\oplus =MAX)\). Zbl 0655.46020Kolokol’tsov, V. N.; Maslov, V. P. 5 1988 Kinetic equations for the pure jump models of \(k\)-nary interacting particle systems. Zbl 1099.60072Kolokoltsov, V. N. 5 2006 Evolutionary inspection and corruption games. Zbl 1406.91039Katsikas, Stamatios; Kolokoltsov, Vassili; Yang, Wei 5 2016 The Lévy-Khintchine type operators with variable Lipschitz continuous coefficients generate linear or nonlinear Markov processes and semigroups. Zbl 1235.60094Kolokoltsov, Vassili N. 5 2011 Understanding game theory. Introduction to the analysis of many agent systems with competition and cooperation. Zbl 1189.91001Kolokoltsov, Vassili N.; Malafeyev, Oleg A. 5 2010 On the solution of two-sided fractional ordinary differential equations of Caputo type. Zbl 1357.34014Hernández-Hernández, Ma. Elena; Kolokoltsov, Vassili N. 5 2016 Idempotent structures in optimization. Zbl 1014.49019Kolokol’tsov, V. N. 4 2001 Hydrodynamic limit of coagulation-fragmentation type models of \(k\)-nary interacting particles. Zbl 1157.82370Kolokoltsov, Vassili N. 4 2004 Measure-valued limits of interacting particle systems with \(k\)-nary interactions. I: One-dimensional limits. Zbl 1038.60094Kolokoltsov, Vassili N. 4 2003 Small time and semiclassical asymptotics for stochastic heat equations driven by Lévy noise. Zbl 1018.60062Kolokol’tsov, V. N.; Tyukov, A. E. 4 2003 Stochastic monotonicity and duality for one-dimensional Markov processes. Zbl 1237.60063Kolokol’tsov, V. N. 4 2011 Quantum mean-field games with the observations of counting type. Zbl 1478.91044Kolokoltsov, Vassili N. 4 2021 Stochastic Hamiltonian-Jacobi-Bellman equation and stochastic Hamiltonian systems. Zbl 0967.60067Kolokoltsov, V. N. 3 1996 Quantization of the Bellman equation, exponential asymptotics and tunneling. Zbl 0796.35141Dobrokhotov, S. Yu.; Kolokoltsov, V. N.; Maslov, V. P. 3 1992 Transience of stochastically perturbed classical Hamiltonian systems and random wave operators. Zbl 0870.60052Albeverio, S.; Hilbert, A.; Kolokoltsov, V. 3 1997 A note on the long time asymptotics of the Brownian motion with application to the theory of quantum measurement. Zbl 0892.60086Kolokoltsov, Vassili N. 3 1997 The rate of escape for some Gaussian processes and the scattering theory for their small perturbations. Zbl 0890.60051Albeverio, Sergio; Kolokoltsov, Vassily N. 3 1997 Stochastic evolution as a quasiclassical limit of a boundary value problem for Schrödinger equations. Zbl 1057.60058Belavkin, V. P.; Kolokol’tsov, V. N. 3 2002 On a general kinetic equation for many-particle systems with interaction, fragmentation and coagulation. Zbl 1070.82022Belavkin, V. P.; Kolokol’tsov, V. N. 3 2003 On the regularity of solutions to the spatially homogeneous Boltzmann equation with polynomially growing collision kernel. Zbl 1132.35338Kolokoltsov, Vassili N. 3 2006 Mixed fractional differential equations and generalized operator-valued Mittag-Leffler functions. Zbl 1439.35538Kolokol’tsov, V. N. 3 2019 Regularity and sensitivity for McKean-Vlasov type SPDEs generated by stable-like processes. Zbl 1423.60101Kolokoltsov, V. N.; Troeva, M. S. 3 2018 A new path integral representation for the solutions of the Schrödinger, heat and stochastic Schrödinger equations. Zbl 1002.35104Kolokoltsov, Vassili N. 2 2002 Transience and non-explosion of certain stochastic Newtonian systems. Zbl 1013.60042Kolokol’tsov, V. N.; Schilling, R. L.; Tyukov, A. E. 2 2002 Estimates for multiple stochastic integrals and stochastic Hamilton-Jacobi equations. Zbl 1060.70025Kolokol’tsov, Vassili N.; Schilling, René L.; Tyukov, Alexei E. 2 2004 Mathematics of the Feynman path integral. Zbl 1055.35054Kolokoltsov, Vassili N. 2 2001 The fractional Hamilton-Jacobi-Bellman equation. Zbl 1365.60049Veretennikova, M.; Kolokoltsov, V. 2 2017 Representation of the solutions of the Belavkin quantum measurement equation by a rigorous version of the Menski functional integration formula. (Représentation des solutions de l’équation de Belavkin pour la mesure quantique par une version rigoureuse de la formule d’intégration fonctionnelle de Menski.) Zbl 0857.60096Albeverio, Sergio; Kolokol’tsov, Vassili N.; Smolyanov, Oleg G. 2 1996 Idempotent analysis as a tool of control theory and optimal synthesis. II. Zbl 0709.49015Kolokol’tsov, V. N.; Maslov, V. P. 2 1989 The Cauchy problem for the homogeneous Bellman equation. Zbl 0666.35018Kolokol’tsov, V. N.; Maslov, V. P. 2 1988 Idempotent analysis as a tool of control theory and optimal synthesis. I. Zbl 0692.49022Kolokol’tsov, V. N.; Maslov, V. P. 2 1989 An approximate Nash equilibrium for pure jump Markov games of mean-field-type on continuous state space. Zbl 1395.91031Basna, Rani; Hilbert, Astrid; Kolokoltsov, Vassili N. 2 2017 Uniform asymptotic bounds for the heat kernel and the trace of a stochastic geodesic flow. Zbl 1259.58012Albeverio, Sergio; Hilbert, Astrid; Kolokoltsov, Vassily 2 2012 The central limit theorem for the Smoluchovski coagulation model. Zbl 1195.82057Kolokoltsov, Vassili N. 2 2010 Pricing of rainbow options: game theoretic approach. Zbl 1213.91154Hucki, Z.; Kolokoltsov, V. N. 2 2007 Understanding game theory. Introduction to the analysis of many agent systems with competition and cooperation. 2nd edition. Zbl 1460.91005Kolokoltsov, Vassili N.; Malafeyev, Oleg A. 2 2021 Nonlinear diffusions and stable-like processes with coefficients depending on the median or var. Zbl 1273.49031Kolokoltsov, Vassili N. 2 2013 The law of large numbers for quantum stochastic filtering and control of many-particle systems. Zbl 1471.81056Kolokoltsov, V. N. 2 2021 The rate of escape of stable Ornstein-Uhlenbeck processes and the scattering theory for their perturbations. Zbl 0993.60088Kolokol’tsov, V. N.; Tyukov, A. E. 1 2001 Mean field games based on stable-like processes. Zbl 1287.91019Kolokol’tsov, Vassiliĭ N.; Troeva, Marianna S.; Yang, Wei 1 2013 On the asymptotic behaviour of the kernel associated by a degenerated diffusion. (Sur le comportement asymptotique du noyau associé à une diffusion dégénérée.) Zbl 0970.35010Albeverio, Sergio; Hilbert, Astrid; Kolokoltsov, Vassily 1 2000 On the asymptotics of low eigenvalues and eigenfunctions of the Schrödinger operator. Zbl 0828.35033Kolokol’tsov, V. N. 1 1993 Schrödinger operators with singular potentials and magnetic fields. Zbl 1069.35064Kolokol’tsov, V. N. 1 2003 Generalized mass action law and thermodynamics of nonlinear Markov processes. Zbl 1327.80015Gorban, A. N.; Kolokoltsov, V. N. 1 2015 Fractionally stable distributions. Zbl 1201.76215Bening, V. E.; Korolev, V. Yu.; Sukhorukova, T. A.; Gusarov, G. G.; Saenko, V. V.; Uchaikin, V. V.; Kolokoltsov, V. N. 1 2006 External pressure on alliances: what does the prisoners’ dilemma reveal? Zbl 1314.91153Binner, Jane M.; Fletcher, Leslie R.; Kolokoltsov, Vassili; Ciardiello, Francesco 1 2013 Introduction of a new Maslov-type currency (coupons) as a means of solving a market game under nonequilibrium prices. Zbl 0792.90012Kolokol’tsov, V. N. 1 1991 Stochastic monotonicity and duality of \(k\)th order with application to put-call symmetry of powered options. Zbl 1344.60074Kolokoltsov, Vassili N. 1 2015 Asymptotically stable invariant tori of a vector field \(V(x)\) and the quasimodes of the operators \(V(x) \cdot \nabla- \varepsilon \Delta\). Zbl 0874.35101Dobrokhotov, S. Yu.; Kolokol’tsov, V. N.; Martines Olive, Victor 1 1995 On extensions of mollified Boltzmann and Smoluchowski equations to particle systems with a \(k\)-ary interaction. Zbl 1039.82029Kolokoltsov, Vassili N. 1 2003 Measure-valued limits of interacting particle systems with \(k\)-nary interactions. II. Finite-dimensional limits. Zbl 1080.60093Kolokoltsov, Vassili N. 1 2004 Quasimodes of the diffusion operator \(-\varepsilon\Delta + v(x)\nabla\), corresponding to asymptotically stable limit cycles of the field \(v(x)\). Zbl 0874.35100Dobrokhotov, Sergei Yu.; Kolokoltsov, Vassili N.; Olivé, Víctor M. 1 1994 The stochastic HJB equation and WKB method. Zbl 0899.35128Kolokoltsov, Vassili N. 1 1998 Turnpikes and infinite extremals in Markov decision processes. Zbl 0692.90102Kolokol’tsov, V. N. 1 1989 Stochastic integrals and SDE driven by nonlinear Lévy noise. Zbl 1227.60096Kolokoltsov, Vassili N. 1 2011 The optimal assignment problem for a countable state space. Zbl 1179.90205Akian, Marianne; Gaubert, Stéphane; Kolokoltsov, Vassili 1 2009 Monte Carlo estimation of the solution of fractional partial differential equations. Zbl 1488.65533Kolokoltsov, Vassili; Lin, Feng; Mijatović, Aleksandar 1 2021 On the probabilistic approach to the solution of generalized fractional differential equations of Caputo and Riemann-Liouville type. Zbl 1488.34038Hernández-Hernández, M. E.; Kolokoltsov, V. N. 1 2016 Probabilistic solutions to nonlinear fractional differential equations of generalized Caputo and Riemann-Liouville type. Zbl 07550684Hernández-Hernández, M. E.; Kolokoltsov, V. N. 1 2018 Quantum mean-field games with the observations of counting type. Zbl 1478.91044Kolokoltsov, Vassili N. 4 2021 Understanding game theory. Introduction to the analysis of many agent systems with competition and cooperation. 2nd edition. Zbl 1460.91005Kolokoltsov, Vassili N.; Malafeyev, Oleg A. 2 2021 The law of large numbers for quantum stochastic filtering and control of many-particle systems. Zbl 1471.81056Kolokoltsov, V. N. 2 2021 Monte Carlo estimation of the solution of fractional partial differential equations. Zbl 1488.65533Kolokoltsov, Vassili; Lin, Feng; Mijatović, Aleksandar 1 2021 On mean field games with common noise and McKean-Vlasov SPDEs. Zbl 1415.60075Kolokoltsov, Vassili N.; Troeva, Marianna 13 2019 The probabilistic point of view on the generalized fractional partial differential equations. Zbl 1483.35002Kolokoltsov, Vassili N. 10 2019 Many agent games in socio-economic systems: corruption, inspection, coalition building, network growth, security. Zbl 1431.91004Kolokoltsov, Vassili N.; Malafeyev, Oleg A. 10 2019 Differential equations on measures and functional spaces. Zbl 1451.34001Kolokoltsov, Vassili 8 2019 Mixed fractional differential equations and generalized operator-valued Mittag-Leffler functions. Zbl 1439.35538Kolokol’tsov, V. N. 3 2019 Regularity and sensitivity for McKean-Vlasov type SPDEs generated by stable-like processes. Zbl 1423.60101Kolokoltsov, V. N.; Troeva, M. S. 3 2018 Probabilistic solutions to nonlinear fractional differential equations of generalized Caputo and Riemann-Liouville type. Zbl 07550684Hernández-Hernández, M. E.; Kolokoltsov, V. N. 1 2018 Generalised fractional evolution equations of Caputo type. Zbl 1374.34009Hernández-Hernández, M. E.; Kolokoltsov, V. N.; Toniazzi, L. 15 2017 Mean-field-game model of corruption. Zbl 1391.91030Kolokoltsov, V. N.; Malafeyev, O. A. 11 2017 The evolutionary game of pressure (or interference), resistance and collaboration. Zbl 1386.91028Kolokoltsov, Vassili 7 2017 The fractional Hamilton-Jacobi-Bellman equation. Zbl 1365.60049Veretennikova, M.; Kolokoltsov, V. 2 2017 An approximate Nash equilibrium for pure jump Markov games of mean-field-type on continuous state space. Zbl 1395.91031Basna, Rani; Hilbert, Astrid; Kolokoltsov, Vassili N. 2 2017 Mean-field-game model for botnet defense in cyber-security. Zbl 1372.49049Kolokoltsov, V. N.; Bensoussan, A. 8 2016 Evolutionary inspection and corruption games. Zbl 1406.91039Katsikas, Stamatios; Kolokoltsov, Vassili; Yang, Wei 5 2016 On the solution of two-sided fractional ordinary differential equations of Caputo type. Zbl 1357.34014Hernández-Hernández, Ma. Elena; Kolokoltsov, Vassili N. 5 2016 On the probabilistic approach to the solution of generalized fractional differential equations of Caputo and Riemann-Liouville type. Zbl 1488.34038Hernández-Hernández, M. E.; Kolokoltsov, V. N. 1 2016 On fully mixed and multidimensional extensions of the Caputo and Riemann-Liouville derivatives, related Markov processes and fractional differential equations. Zbl 1321.26013Kolokoltsov, Vassili 18 2015 Generalized mass action law and thermodynamics of nonlinear Markov processes. Zbl 1327.80015Gorban, A. N.; Kolokoltsov, V. N. 1 2015 Stochastic monotonicity and duality of \(k\)th order with application to put-call symmetry of powered options. Zbl 1344.60074Kolokoltsov, Vassili N. 1 2015 On the rate of convergence for the mean-field approximation of controlled diffusions with large number of players. Zbl 1314.91020Kolokoltsov, Vassili N.; Troeva, Marianna; Yang, Wei 18 2014 Well-posedness and regularity of the Cauchy problem for nonlinear fractional in time and space equations. Zbl 1412.35370Kolokoltsov, V. N.; Veretennikova, M. A. 13 2014 A fractional Hamilton Jacobi Bellman equation for scaled limits of controlled continuous time random walks. Zbl 1329.60117Kolokoltsov, Vassili N.; Veretennikova, Maria A. 12 2014 The interval market model in mathematical finance. Game-theoretic methods. Zbl 1279.91005Bernhard, Pierre; Engwerda, Jacob C.; Roorda, Berend; Schumacher, Johannes M.; Kolokoltsov, Vassili; Saint-Pierre, Patrick; Aubin, Jean-Pierre 12 2013 Stochastic duality of Markov processes: A study via generators. Zbl 1291.60154Kolokoltsov, Vassili; Lee, Rui Xin 6 2013 Nonlinear diffusions and stable-like processes with coefficients depending on the median or var. Zbl 1273.49031Kolokoltsov, Vassili N. 2 2013 Mean field games based on stable-like processes. Zbl 1287.91019Kolokol’tsov, Vassiliĭ N.; Troeva, Marianna S.; Yang, Wei 1 2013 External pressure on alliances: what does the prisoners’ dilemma reveal? Zbl 1314.91153Binner, Jane M.; Fletcher, Leslie R.; Kolokoltsov, Vassili; Ciardiello, Francesco 1 2013 Turnpike theorems for Markov games. Zbl 1272.91027Kolokoltsov, Vassili; Yang, Wei 12 2012 Uniform asymptotic bounds for the heat kernel and the trace of a stochastic geodesic flow. Zbl 1259.58012Albeverio, Sergio; Hilbert, Astrid; Kolokoltsov, Vassily 2 2012 Markov processes, semigroups and generators. Zbl 1220.60003Kolokoltsov, Vassili N. 70 2011 The Lévy-Khintchine type operators with variable Lipschitz continuous coefficients generate linear or nonlinear Markov processes and semigroups. Zbl 1235.60094Kolokoltsov, Vassili N. 5 2011 Stochastic monotonicity and duality for one-dimensional Markov processes. Zbl 1237.60063Kolokol’tsov, V. N. 4 2011 Stochastic integrals and SDE driven by nonlinear Lévy noise. Zbl 1227.60096Kolokoltsov, Vassili N. 1 2011 Nonlinear Markov processes and kinetic equations. Zbl 1222.60003Kolokoltsov, Vassili N. 67 2010 Understanding game theory. Introduction to the analysis of many agent systems with competition and cooperation. Zbl 1189.91001Kolokoltsov, Vassili N.; Malafeyev, Oleg A. 5 2010 The central limit theorem for the Smoluchovski coagulation model. Zbl 1195.82057Kolokoltsov, Vassili N. 2 2010 Generalized continuous-time random walks, subordination by hitting times, and fractional dynamics. Zbl 1193.60046Kolokoltsov, V. N. 33 2009 The optimal assignment problem for a countable state space. Zbl 1179.90205Akian, Marianne; Gaubert, Stéphane; Kolokoltsov, Vassili 1 2009 Nonlinear Markov semigroups and interacting Lévy type processes. Zbl 1110.82029Kolokoltsov, Vassili N. 9 2007 Pricing of rainbow options: game theoretic approach. Zbl 1213.91154Hucki, Z.; Kolokoltsov, V. N. 2 2007 Kinetic equations for the pure jump models of \(k\)-nary interacting particle systems. Zbl 1099.60072Kolokoltsov, V. N. 5 2006 On the regularity of solutions to the spatially homogeneous Boltzmann equation with polynomially growing collision kernel. Zbl 1132.35338Kolokoltsov, Vassili N. 3 2006 Fractionally stable distributions. Zbl 1201.76215Bening, V. E.; Korolev, V. Yu.; Sukhorukova, T. A.; Gusarov, G. G.; Saenko, V. V.; Uchaikin, V. V.; Kolokoltsov, V. N. 1 2006 Set coverings and invertibility of functional Galois connections. Zbl 1080.06001Akian, Marianne; Gaubert, Stéphane; Kolokoltsov, Vassili 10 2005 On Markov processes with decomposable pseudo-differential generators. Zbl 1091.60014Kolokoltsov, Vassili N. 10 2004 Estimation of parameters of fractional stable distributions. Zbl 1130.62023Bening, V. E.; Korolev, V. Yu.; Kolokol’tsov, V. N.; Saenko, V. V.; Uchaikin, V. V.; Zolotarev, V. M. 5 2004 Hydrodynamic limit of coagulation-fragmentation type models of \(k\)-nary interacting particles. Zbl 1157.82370Kolokoltsov, Vassili N. 4 2004 Estimates for multiple stochastic integrals and stochastic Hamilton-Jacobi equations. Zbl 1060.70025Kolokol’tsov, Vassili N.; Schilling, René L.; Tyukov, Alexei E. 2 2004 Measure-valued limits of interacting particle systems with \(k\)-nary interactions. II. Finite-dimensional limits. Zbl 1080.60093Kolokoltsov, Vassili N. 1 2004 Measure-valued limits of interacting particle systems with \(k\)-nary interactions. I: One-dimensional limits. Zbl 1038.60094Kolokoltsov, Vassili N. 4 2003 Small time and semiclassical asymptotics for stochastic heat equations driven by Lévy noise. Zbl 1018.60062Kolokol’tsov, V. N.; Tyukov, A. E. 4 2003 On a general kinetic equation for many-particle systems with interaction, fragmentation and coagulation. Zbl 1070.82022Belavkin, V. P.; Kolokol’tsov, V. N. 3 2003 Schrödinger operators with singular potentials and magnetic fields. Zbl 1069.35064Kolokol’tsov, V. N. 1 2003 On extensions of mollified Boltzmann and Smoluchowski equations to particle systems with a \(k\)-ary interaction. Zbl 1039.82029Kolokoltsov, Vassili N. 1 2003 Invertibility of functional Galois connections. Zbl 1022.06001Akian, Marianne; Gaubert, Stéphane; Kolokoltsov, Vassili 7 2002 Stochastic evolution as a quasiclassical limit of a boundary value problem for Schrödinger equations. Zbl 1057.60058Belavkin, V. P.; Kolokol’tsov, V. N. 3 2002 A new path integral representation for the solutions of the Schrödinger, heat and stochastic Schrödinger equations. Zbl 1002.35104Kolokoltsov, Vassili N. 2 2002 Transience and non-explosion of certain stochastic Newtonian systems. Zbl 1013.60042Kolokol’tsov, V. N.; Schilling, R. L.; Tyukov, A. E. 2 2002 Fractional stable distributions. Zbl 0994.60010Kolokoltsov, V.; Korolev, V.; Uchaikin, V. 8 2001 Idempotent structures in optimization. Zbl 1014.49019Kolokol’tsov, V. N. 4 2001 Mathematics of the Feynman path integral. Zbl 1055.35054Kolokoltsov, Vassili N. 2 2001 The rate of escape of stable Ornstein-Uhlenbeck processes and the scattering theory for their perturbations. Zbl 0993.60088Kolokol’tsov, V. N.; Tyukov, A. E. 1 2001 Symmetric stable laws and stable-like jump-diffusions. Zbl 1021.60011Kolokoltsov, Vassili 100 2000 Semiclassical analysis for diffusions and stochastic processes. Zbl 0951.60001Kolokoltsov, V. N. 37 2000 On the asymptotic behaviour of the kernel associated by a degenerated diffusion. (Sur le comportement asymptotique du noyau associé à une diffusion dégénérée.) Zbl 0970.35010Albeverio, Sergio; Hilbert, Astrid; Kolokoltsov, Vassily 1 2000 Estimates uniform in time for the transition probability of diffusions with small drift and for stochastically perturbed Newton equations. Zbl 0928.60061Albeverio, Sergio; Hilbert, Astrid; Kolokoltsov, Vassili 5 1999 Nonexpansive maps and option pricing theory. Zbl 1274.91420Kolokoltsov, Vassili N. 17 1998 Localization and analytic properties of the solutions of the simplest quantum filtering equation. Zbl 0927.60088Kolokol’tsov, Vassili N. 6 1998 The stochastic HJB equation and WKB method. Zbl 0899.35128Kolokoltsov, Vassili N. 1 1998 Idempotent analysis and its applications. Appendix by Pierre Del Moral. Transl. from the Russian by V. E. Nazaikinskij. Zbl 0941.93001Kolokoltsov, V. N.; Maslov, V. P. 118 1997 Continuous quantum measurement: Local and global approaches. Zbl 0894.47058Albeverio, S.; Kolokol’tsov, V. N.; Smolyanov, O. G. 6 1997 Transience of stochastically perturbed classical Hamiltonian systems and random wave operators. Zbl 0870.60052Albeverio, S.; Hilbert, A.; Kolokoltsov, V. 3 1997 A note on the long time asymptotics of the Brownian motion with application to the theory of quantum measurement. Zbl 0892.60086Kolokoltsov, Vassili N. 3 1997 The rate of escape for some Gaussian processes and the scattering theory for their small perturbations. Zbl 0890.60051Albeverio, Sergio; Kolokoltsov, Vassily N. 3 1997 Asymptotic spectral analysis of a small diffusion operator and the life times of the corresponding diffusion process. Zbl 0912.58042Kolokol’tsov, Vassili N.; Makarov, Konstantin A. 10 1996 Stochastic Hamiltonian-Jacobi-Bellman equation and stochastic Hamiltonian systems. Zbl 0967.60067Kolokoltsov, V. N. 3 1996 Representation of the solutions of the Belavkin quantum measurement equation by a rigorous version of the Menski functional integration formula. (Représentation des solutions de l’équation de Belavkin pour la mesure quantique par une version rigoureuse de la formule d’intégration fonctionnelle de Menski.) Zbl 0857.60096Albeverio, Sergio; Kolokol’tsov, Vassili N.; Smolyanov, Oleg G. 2 1996 Scattering theory for the Belavkin equation describing a quantum particle with continuously observed coordinate. Zbl 0845.35078Kolokol’tsov, Vassili N. 10 1995 The double-well splitting of the low energy levels for the Schrödinger operator of discrete \(\varphi^ 4\)-models on tori. Zbl 0820.60097Dobrokhotov, Sergei Yu.; Kolokol’tsov, Vassili N. 6 1995 Asymptotically stable invariant tori of a vector field \(V(x)\) and the quasimodes of the operators \(V(x) \cdot \nabla- \varepsilon \Delta\). Zbl 0874.35101Dobrokhotov, S. Yu.; Kolokol’tsov, V. N.; Martines Olive, Victor 1 1995 Idempotent analysis and its applications to optimal control. (Idempotentnyj analiz i ego primenenie v optimal’nom upravlenii.) Zbl 0857.49022Maslov, V. P.; Kolokol’tsov, V. N. 7 1994 Quasimodes of the diffusion operator \(-\varepsilon\Delta + v(x)\nabla\), corresponding to asymptotically stable limit cycles of the field \(v(x)\). Zbl 0874.35100Dobrokhotov, Sergei Yu.; Kolokoltsov, Vassili N.; Olivé, Víctor M. 1 1994 Splitting amplitudes of the lowest energy levels of the Schrödinger operator with double-well potential. Zbl 0799.35050Dobrokhotov, S. Yu.; Kolokol’tsov, V. N. 7 1993 On the asymptotics of low eigenvalues and eigenfunctions of the Schrödinger operator. Zbl 0828.35033Kolokol’tsov, V. N. 1 1993 On linear, additive, and homogeneous operators in idempotent analysis. Zbl 0925.47016Kolokoltsov, V. N. 10 1992 Quantization of the Bellman equation, exponential asymptotics and tunneling. Zbl 0796.35141Dobrokhotov, S. Yu.; Kolokoltsov, V. N.; Maslov, V. P. 3 1992 Splitting of the lowest energy levels of the Schrödinger equation and asymptotic behavior of the fundamental solution of the equation \(hu_ t=h^ 2\Delta u/2-V(x)u\). Zbl 0745.35033Dobrokhotov, S. Yu.; Kolokol’tsov, V. N.; Maslov, V. P. 11 1991 Introduction of a new Maslov-type currency (coupons) as a means of solving a market game under nonequilibrium prices. Zbl 0792.90012Kolokol’tsov, V. N. 1 1991 Idempotent analysis as a tool of control theory and optimal synthesis. I. Zbl 0709.49014Kolokol’tsov, V. N.; Maslov, V. P. 14 1989 Idempotent analysis as a tool of control theory and optimal synthesis. II. Zbl 0709.49015Kolokol’tsov, V. N.; Maslov, V. P. 2 1989 Idempotent analysis as a tool of control theory and optimal synthesis. I. Zbl 0692.49022Kolokol’tsov, V. N.; Maslov, V. P. 2 1989 Turnpikes and infinite extremals in Markov decision processes. Zbl 0692.90102Kolokol’tsov, V. N. 1 1989 The general form of the endomorphisms in the space of continuous functions with values in a numerical commutative semiring (with the operation \(\oplus =MAX)\). Zbl 0655.46020Kolokol’tsov, V. N.; Maslov, V. P. 5 1988 The Cauchy problem for the homogeneous Bellman equation. Zbl 0666.35018Kolokol’tsov, V. N.; Maslov, V. P. 2 1988 Geodesic flows on two-dimensional manifolds with an additional first integral that is polynomial in the velocities. Zbl 0548.58028Kolokol’tsov, V. N. 20 1983 Geodesic flows on two-dimensional manifolds with according to the velocities complementary polynomial first integral. Zbl 0518.58033Kolokol’tsov, V. N. 11 1982 all cited Publications top 5 cited Publications all top 5 Cited by 808 Authors 43 Kolokoltsov, Vassili N. 23 Gaubert, Stéphane 13 Albeverio, Sergio A. 13 Chen, Zhen-Qing 11 Schilling, René Leander 10 Pap, Endre 9 Akian, Marianne 9 Maslov, Viktor Pavlovich 9 Meerschaert, Mark Marvin 9 Menozzi, Stéphane 8 Bass, Richard F. 8 Krivulin, Nikolai K. 8 McEneaney, William “Mac” M. 8 Smirnov, Sergeĭ Nikolaevich 8 Štrboja, Mirjana 8 Wang, Jian 8 Wu, Jianglun 7 Averboukh, Yuriĭ Vladimirovich 7 Kondrat’yev, Yuriĭ Grygorovych 7 Matveev, Vladimir S. 7 Pavlyukevich, Ilya 7 Ricciuti, Costantino 7 Sandrić, Nikola 7 Zaslavski, Alexander Yakovlevich 6 Katz, Ricardo David 6 Knopova, Victoria Pavlovna 6 Leonenko, Nikolai N. 6 Liu, Junfeng 6 Saburov, Mansoor 6 Sergeev, Sergeĭ Mikhaĭlovich 6 Štajner-Papuga, Ivana 6 Toaldo, Bruno 5 Allamigeon, Xavier 5 Bäumer, Boris 5 Bolsinov, Alexey V. 5 Cavazos-Cadena, Rolando 5 Grbić, Tatjana 5 Kühn, Franziska 5 Peperko, Aljoša 5 Troeva, Marianna S. 5 Yan, Litan 4 Agapov, Sergei Vadimovich 4 Anikin, A. Yu. 4 Dobrokhotov, Sergei Yurievich 4 Fujii, Masaaki 4 Kovács, Mihály 4 Kulik, Alexey M. 4 Kumagai, Takashi 4 Kutoviy, Oleksandr V. 4 Mazzucchi, Sonia 4 Mesiar, Radko 4 Orsingher, Enzo 4 Plavka, Ján 4 Pucacco, Giuseppe 4 Roquejoffre, Jean-Michel 4 Saburov, Mansur Kh. 4 Sikorskii, Alla 4 Straka, Peter 4 Toniazzi, Lorenzo 4 Truman, Aubrey 4 Wu, Ruoyu 3 Agahi, Hamzeh 3 Aida, Shigeki 3 Anh, Vo V. 3 Ascione, Giacomo 3 Beghin, Luisa 3 Bennett, Jonathan 3 Bensoussan, Alain 3 Butkovič, Peter 3 Chaudru De Raynal, Paul-Eric 3 Clement, Emmanuelle 3 Di Nola, Antonio 3 Dower, Peter M. 3 Duan, Jinqiao 3 Finkelshteĭn, Dmitriĭ Leonidovich 3 Fomenko, Anatoliĭ Timofeevich 3 Foondun, Mohammud 3 Frikha, Noufel 3 Gomes, Diogo Luís Aguiar 3 Hernández-Hernández, Daniel 3 Hernández-Hernández, Ma. Elena 3 Hilbert, Astrid 3 Hochart, Antoine 3 Kaßmann, Moritz 3 Khlopin, Dmitriĭ Valer’evich 3 Kim, Panki 3 Kochubeĭ, Anatoliĭ Naumovych 3 Konakov, Valentin 3 Łapiński, Tomasz M. 3 Litvinov, Grigory Lazarevich 3 Liu, Jianguo 3 Mihailović, Biljana P. 3 Mora, Carlos M. 3 Müller, Vladimír 3 Nguyen, Son Luu 3 Papić, Ivan 3 Pirozzi, Enrica 3 Priola, Enrico 3 Pułka, Małgorzata 3 Rosquist, Kjell ...and 708 more Authors all top 5 Cited in 222 Serials 28 Stochastic Processes and their Applications 19 Mathematical Notes 19 Linear Algebra and its Applications 18 Fractional Calculus & Applied Analysis 16 Fuzzy Sets and Systems 14 Applied Mathematics and Optimization 14 Journal of Theoretical Probability 13 Transactions of the American Mathematical Society 13 Journal of Mathematical Sciences (New York) 11 Journal of Functional Analysis 11 Nonlinear Analysis. Theory, Methods & Applications. 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Komp’yuternye Nauki 2 International Journal of Modern Physics A 2 Advances in Applied Probability 2 Communications in Algebra 2 Bulletin of Mathematical Biology 2 Advances in Mathematics 2 International Journal of Game Theory 2 Journal of the Mathematical Society of Japan 2 Mathematische Annalen 2 Mathematics of Operations Research 2 Mathematica Slovaca 2 Results in Mathematics 2 Semigroup Forum 2 Physica D 2 International Journal of Approximate Reasoning 2 Computational Mathematics and Modeling 2 Annals of Operations Research 2 Discrete Event Dynamic Systems 2 European Journal of Operational Research 2 SIAM Journal on Mathematical Analysis 2 Fractals 2 Journal of Convex Analysis 2 Mathematical Problems in Engineering 2 Finance and Stochastics 2 Doklady Mathematics 2 Regular and Chaotic Dynamics 2 Differential Equations 2 Journal of Evolution Equations 2 Dynamics of Continuous, Discrete & Impulsive Systems. Series B. Applications & Algorithms 2 Comptes Rendus. Mathématique. 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