Edit Profile (opens in new tab) Kolokoltsov, Vassili N. Co-Author Distance 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: 147 Publications since 1982, including 10 Books and 16 Additional arXiv Preprints 1 Contribution as Editor Co-Authors: 78 Co-Authors with 83 Joint Publications 2,824 Co-Co-Authors all top 5 Co-Authors 63 single-authored 11 Maslov, Viktor Pavlovich 8 Troeva, Marianna S. 7 Albeverio, Sergio A. 7 Hilbert, Astrid 7 Yang, Wei 6 Dobrokhotov, Sergei Yurievich 6 Malafeev, Oleg Alekseivich 4 Akian, Marianne 4 Binner, Jane M. 4 Fletcher, Leslie R. 4 Gaubert, Stéphane 4 Hernández-Hernández, Ma. Elena 4 Korolev, Viktor Yur’evich 4 Veretennikova, Maria A. 3 Bening, Vladimir E. 3 Ciardiello, Francesco 3 Uchaĭkin, Vladimir Vasil’evich 2 Basna, Rani 2 Belavkin, Viacheslav 2 Johnston, Ifan 2 Saenko, Viacheslav V. 2 Schilling, René Leander 2 Smolyanov, Oleg Georgievich 1 Ageev, Oleg N. 1 Al-Talibi, Haidar 1 Aubin, Jean-Pierre 1 Ball, Robin C. 1 Bensoussan, Alain 1 Bernhard, Pierre 1 Cecchin, Alekos 1 Del Moral, Pierre 1 Dranov, Egor M. 1 Efremova, Lyudmila S. 1 Engwerda, Jacob Christiaan 1 Gorban, Alexander N. 1 Grigorchuk, Rostislav Ivanovich 1 Grines, Vyacheslav Zigmundovich 1 Gurevich, Boris 1 Gusarov, G. G. 1 Khelemskiĭ, Aleksandr Yakovlevich 1 Hucki, Z. 1 Kashin, Boris Sergeevich 1 Katsikas, Stamatios 1 Khodarinova, L. A. 1 Kochergin, Andrey V. 1 Lebedev, Dmitrii R. 1 Lee, Rui Xin 1 Lerman, Lev 1 Li, Jiajie 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 Piskun, Denis E. 1 Pochinka, Ol’ga Vital’evna 1 Roorda, Berend 1 Ryzhikov, Valeriĭ Valentinovich 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 Tikhonov, Sergei Viktorovich 1 Toniazzi, Lorenzo 1 Tyukov, Alexei E. 1 Tyukov, Alexey E. 1 Vorobets, Yaroslav 1 Weiss, Benjamin 1 Whysall, P. 1 Zhirov, Aleksei Yu. 1 Zolotarëv, Vladimir Mikhaĭlovich all top 5 Serials 5 Mathematical Notes 5 Fractional Calculus & Applied Analysis 4 Stochastics and Stochastics Reports 4 Journal of Mathematical Sciences (New York) 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 69 Probability theory and stochastic processes (60-XX) 42 Partial differential equations (35-XX) 36 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 27 Quantum theory (81-XX) 24 Calculus of variations and optimal control; optimization (49-XX) 16 Statistical mechanics, structure of matter (82-XX) 12 Operations research, mathematical programming (90-XX) 11 Operator theory (47-XX) 10 Ordinary differential equations (34-XX) 9 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) 3 Order, lattices, ordered algebraic structures (06-XX) 3 Special functions (33-XX) 3 Integral transforms, operational calculus (44-XX) 2 Statistics (62-XX) 2 Numerical analysis (65-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 Classical thermodynamics, heat transfer (80-XX) 1 Biology and other natural sciences (92-XX) 1 Information and communication theory, circuits (94-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 108 Publications have been cited 1,339 times in 932 Documents Cited by ▼ Year ▼ Idempotent analysis and its applications. Appendix by Pierre Del Moral. Transl. from the Russian by V. E. Nazaikinskij. Zbl 0941.93001 Kolokoltsov, V. N.; Maslov, V. P. 160 1997 Nonlinear Markov processes and kinetic equations. Zbl 1222.60003 Kolokoltsov, Vassili N. 123 2010 Symmetric stable laws and stable-like jump-diffusions. Zbl 1021.60011 Kolokoltsov, Vassili 118 2000 Markov processes, semigroups and generators. Zbl 1220.60003 Kolokoltsov, Vassili N. 104 2011 Semiclassical analysis for diffusions and stochastic processes. Zbl 0951.60001 Kolokoltsov, V. N. 47 2000 Generalized continuous-time random walks, subordination by hitting times, and fractional dynamics. Zbl 1193.60046 Kolokoltsov, V. N. 42 2009 Idempotent analysis and its applications to optimal control. (Idempotentnyj analiz i ego primenenie v optimal’nom upravlenii.) Zbl 0857.49022 Maslov, V. P.; Kolokol’tsov, V. N. 29 1994 Geodesic flows on two-dimensional manifolds with an additional first integral that is polynomial in the velocities. Zbl 0548.58028 Kolokol’tsov, V. N. 29 1983 On fully mixed and multidimensional extensions of the Caputo and Riemann-Liouville derivatives, related Markov processes and fractional differential equations. Zbl 1321.26013 Kolokoltsov, Vassili 24 2015 Mean-field-game model of corruption. Zbl 1391.91030 Kolokoltsov, V. N.; Malafeyev, O. A. 23 2017 Well-posedness and regularity of the Cauchy problem for nonlinear fractional in time and space equations. Zbl 1412.35370 Kolokoltsov, V. N.; Veretennikova, M. A. 22 2014 Nonexpansive maps and option pricing theory. Zbl 1274.91420 Kolokoltsov, Vassili N. 21 1998 The probabilistic point of view on the generalized fractional partial differential equations. Zbl 1483.35002 Kolokoltsov, Vassili N. 21 2019 Idempotent analysis as a tool of control theory and optimal synthesis. I. Zbl 0709.49014 Kolokol’tsov, V. N.; Maslov, V. P. 19 1989 Generalised fractional evolution equations of Caputo type. Zbl 1374.34009 Hernández-Hernández, M. E.; Kolokoltsov, V. N.; Toniazzi, L. 19 2017 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 0745.35033 Dobrokhotov, S. Yu.; Kolokol’tsov, V. N.; Maslov, V. P. 18 1991 On the rate of convergence for the mean-field approximation of controlled diffusions with large number of players. Zbl 1314.91020 Kolokoltsov, Vassili N.; Troeva, Marianna; Yang, Wei 18 2014 Mean-field-game model for botnet defense in cyber-security. Zbl 1372.49049 Kolokoltsov, V. N.; Bensoussan, A. 18 2016 Many agent games in socio-economic systems: corruption, inspection, coalition building, network growth, security. Zbl 1431.91004 Kolokoltsov, Vassili N.; Malafeyev, Oleg A. 18 2019 Differential equations on measures and functional spaces. Zbl 1451.34001 Kolokoltsov, Vassili 18 2019 On mean field games with common noise and McKean-Vlasov SPDEs. Zbl 1415.60075 Kolokoltsov, Vassili N.; Troeva, Marianna 18 2019 A fractional Hamilton Jacobi Bellman equation for scaled limits of controlled continuous time random walks. Zbl 1329.60117 Kolokoltsov, Vassili N.; Veretennikova, Maria A. 17 2014 The interval market model in mathematical finance. Game-theoretic methods. Zbl 1279.91005 Bernhard, Pierre; Engwerda, Jacob C.; Roorda, Berend; Schumacher, Johannes M.; Kolokoltsov, Vassili; Saint-Pierre, Patrick; Aubin, Jean-Pierre 16 2013 Splitting amplitudes of the lowest energy levels of the Schrödinger operator with double-well potential. Zbl 0799.35050 Dobrokhotov, S. Yu.; Kolokol’tsov, V. N. 15 1993 Set coverings and invertibility of functional Galois connections. Zbl 1080.06001 Akian, Marianne; Gaubert, Stéphane; Kolokoltsov, Vassili 14 2005 Turnpike theorems for Markov games. Zbl 1272.91027 Kolokoltsov, Vassili; Yang, Wei 14 2012 Geodesic flows on two-dimensional manifolds with according to the velocities complementary polynomial first integral. Zbl 0518.58033 Kolokol’tsov, V. N. 13 1982 Fractional stable distributions. Zbl 0994.60010 Kolokoltsov, V.; Korolev, V.; Uchaikin, V. 11 2001 On linear, additive, and homogeneous operators in idempotent analysis. Zbl 0925.47016 Kolokoltsov, V. N. 11 1992 Asymptotic spectral analysis of a small diffusion operator and the life times of the corresponding diffusion process. Zbl 0912.58042 Kolokol’tsov, Vassili N.; Makarov, Konstantin A. 11 1996 Nonlinear Markov semigroups and interacting Lévy type processes. Zbl 1110.82029 Kolokoltsov, Vassili N. 10 2007 On Markov processes with decomposable pseudo-differential generators. Zbl 1091.60014 Kolokoltsov, Vassili N. 10 2004 Scattering theory for the Belavkin equation describing a quantum particle with continuously observed coordinate. Zbl 0845.35078 Kolokol’tsov, Vassili N. 10 1995 Idempotent analysis as a tool of control theory and optimal synthesis. II. Zbl 0709.49015 Kolokol’tsov, V. N.; Maslov, V. P. 9 1989 Idempotent analysis as a tool of control theory and optimal synthesis. I. Zbl 0692.49022 Kolokol’tsov, V. N.; Maslov, V. P. 9 1989 The evolutionary game of pressure (or interference), resistance and collaboration. Zbl 1386.91028 Kolokoltsov, Vassili 9 2017 Understanding game theory. Introduction to the analysis of many agent systems with competition and cooperation. Zbl 1189.91001 Kolokoltsov, Vassili N.; Malafeyev, Oleg A. 9 2010 The double-well splitting of the low energy levels for the Schrödinger operator of discrete \(\varphi^ 4\)-models on tori. Zbl 0820.60097 Dobrokhotov, Sergei Yu.; Kolokol’tsov, Vassili N. 8 1995 On a general kinetic equation for many-particle systems with interaction, fragmentation and coagulation. Zbl 1070.82022 Belavkin, V. P.; Kolokol’tsov, V. N. 8 2003 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 0655.46020 Kolokol’tsov, V. N.; Maslov, V. P. 7 1988 Continuous quantum measurement: Local and global approaches. Zbl 0894.47058 Albeverio, S.; Kolokol’tsov, V. N.; Smolyanov, O. G. 7 1997 Idempotent structures in optimization. Zbl 1014.49019 Kolokol’tsov, V. N. 7 2001 Kinetic equations for the pure jump models of \(k\)-nary interacting particle systems. Zbl 1099.60072 Kolokoltsov, V. N. 7 2006 The Lévy-Khintchine type operators with variable Lipschitz continuous coefficients generate linear or nonlinear Markov processes and semigroups. Zbl 1235.60094 Kolokoltsov, Vassili N. 7 2011 Invertibility of functional Galois connections. Zbl 1022.06001 Akian, Marianne; Gaubert, Stéphane; Kolokoltsov, Vassili 7 2002 Localization and analytic properties of the solutions of the simplest quantum filtering equation. Zbl 0927.60088 Kolokol’tsov, Vassili N. 7 1998 An approximate Nash equilibrium for pure jump Markov games of mean-field-type on continuous state space. Zbl 1395.91031 Basna, Rani; Hilbert, Astrid; Kolokoltsov, Vassili N. 6 2017 Stochastic monotonicity and duality for one-dimensional Markov processes. Zbl 1237.60063 Kolokol’tsov, V. N. 6 2011 Estimation of parameters of fractional stable distributions. Zbl 1130.62023 Bening, V. E.; Korolev, V. Yu.; Kolokol’tsov, V. N.; Saenko, V. V.; Uchaikin, V. V.; Zolotarev, V. M. 6 2004 Evolutionary inspection and corruption games. Zbl 1406.91039 Katsikas, Stamatios; Kolokoltsov, Vassili; Yang, Wei 6 2016 Stochastic duality of Markov processes: A study via generators. Zbl 1291.60154 Kolokoltsov, Vassili; Lee, Rui Xin 6 2013 On the probabilistic approach to the solution of generalized fractional differential equations of Caputo and Riemann-Liouville type. Zbl 1488.34038 Hernández-Hernández, M. E.; Kolokoltsov, V. N. 6 2016 The stochastic Bellman equation as a nonlinear equation in Maslov spaces. Perturbation theory. Zbl 0802.49022 Kolokol’tsov, V. N. 5 1992 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 0857.60096 Albeverio, Sergio; Kolokol’tsov, Vassili N.; Smolyanov, Oleg G. 5 1996 Estimates uniform in time for the transition probability of diffusions with small drift and for stochastically perturbed Newton equations. Zbl 0928.60061 Albeverio, Sergio; Hilbert, Astrid; Kolokoltsov, Vassili 5 1999 Quantum mean-field games with the observations of counting type. Zbl 1478.91044 Kolokoltsov, Vassili N. 5 2021 Regularity and sensitivity for McKean-Vlasov type SPDEs generated by stable-like processes. Zbl 1423.60101 Kolokoltsov, V. N.; Troeva, M. S. 5 2018 On the solution of two-sided fractional ordinary differential equations of Caputo type. Zbl 1357.34014 Hernández-Hernández, Ma. Elena; Kolokoltsov, Vassili N. 5 2016 Corruption and botnet defense: a mean field game approach. Zbl 1417.91074 Kolokoltsov, V. N.; Malafeyev, O. A. 4 2018 Hydrodynamic limit of coagulation-fragmentation type models of \(k\)-nary interacting particles. Zbl 1157.82370 Kolokoltsov, Vassili N. 4 2004 Stochastic evolution as a quasiclassical limit of a boundary value problem for Schrödinger equations. Zbl 1057.60058 Belavkin, V. P.; Kolokol’tsov, V. N. 4 2002 Small time and semiclassical asymptotics for stochastic heat equations driven by Lévy noise. Zbl 1018.60062 Kolokol’tsov, V. N.; Tyukov, A. E. 4 2003 Quantization of the Bellman equation, exponential asymptotics and tunneling. Zbl 0796.35141 Dobrokhotov, S. Yu.; Kolokoltsov, V. N.; Maslov, V. P. 4 1992 Measure-valued limits of interacting particle systems with \(k\)-nary interactions. I: One-dimensional limits. Zbl 1038.60094 Kolokoltsov, Vassili N. 4 2003 Understanding game theory. Introduction to the analysis of many agent systems with competition and cooperation. 2nd edition. Zbl 1460.91005 Kolokoltsov, Vassili N.; Malafeyev, Oleg A. 4 2021 Mixed fractional differential equations and generalized operator-valued Mittag-Leffler functions. Zbl 1439.35538 Kolokol’tsov, V. N. 4 2019 Transience of stochastically perturbed classical Hamiltonian systems and random wave operators. Zbl 0870.60052 Albeverio, S.; Hilbert, A.; Kolokoltsov, V. 3 1997 The rate of escape for some Gaussian processes and the scattering theory for their small perturbations. Zbl 0890.60051 Albeverio, Sergio; Kolokoltsov, Vassily N. 3 1997 The fractional Hamilton-Jacobi-Bellman equation. Zbl 1365.60049 Veretennikova, M.; Kolokoltsov, V. 3 2017 Mean field games based on stable-like processes. Zbl 1287.91019 Kolokol’tsov, Vassiliĭ N.; Troeva, Marianna S.; Yang, Wei 3 2013 Uniform asymptotic bounds for the heat kernel and the trace of a stochastic geodesic flow. Zbl 1259.58012 Albeverio, Sergio; Hilbert, Astrid; Kolokoltsov, Vassily 3 2012 The central limit theorem for the Smoluchovski coagulation model. Zbl 1195.82057 Kolokoltsov, Vassili N. 3 2010 Stochastic Hamiltonian-Jacobi-Bellman equation and stochastic Hamiltonian systems. Zbl 0967.60067 Kolokoltsov, V. N. 3 1996 Transience and non-explosion of certain stochastic Newtonian systems. Zbl 1013.60042 Kolokol’tsov, V. N.; Schilling, R. L.; Tyukov, A. E. 3 2002 On the regularity of solutions to the spatially homogeneous Boltzmann equation with polynomially growing collision kernel. Zbl 1132.35338 Kolokoltsov, Vassili N. 3 2006 A note on the long time asymptotics of the Brownian motion with application to the theory of quantum measurement. Zbl 0892.60086 Kolokoltsov, Vassili N. 3 1997 Nonlinear diffusions and stable-like processes with coefficients depending on the median or var. Zbl 1273.49031 Kolokoltsov, Vassili N. 3 2013 Probabilistic solutions to nonlinear fractional differential equations of generalized Caputo and Riemann-Liouville type. Zbl 1498.60284 Hernández-Hernández, M. E.; Kolokoltsov, V. N. 3 2018 The law of large numbers for quantum stochastic filtering and control of many-particle systems. Zbl 1471.81056 Kolokoltsov, V. N. 3 2021 Nonlinear Lévy and nonlinear Feller processes: an analytic introduction. Zbl 1462.60066 Kolokoltsov, Vassili N. 3 2013 The Cauchy problem for the homogeneous Bellman equation. Zbl 0666.35018 Kolokol’tsov, V. N.; Maslov, V. P. 2 1988 Turnpikes and infinite extremals in Markov decision processes. Zbl 0692.90102 Kolokol’tsov, V. N. 2 1989 Fractionally stable distributions. Zbl 1201.76215 Bening, V. E.; Korolev, V. Yu.; Sukhorukova, T. A.; Gusarov, G. G.; Saenko, V. V.; Uchaikin, V. V.; Kolokoltsov, V. N. 2 2006 A new path integral representation for the solutions of the Schrödinger, heat and stochastic Schrödinger equations. Zbl 1002.35104 Kolokoltsov, Vassili N. 2 2002 Estimates for multiple stochastic integrals and stochastic Hamilton-Jacobi equations. Zbl 1060.70025 Kolokol’tsov, Vassili N.; Schilling, René L.; Tyukov, Alexei E. 2 2004 Mathematics of the Feynman path integral. Zbl 1055.35054 Kolokoltsov, Vassili N. 2 2001 Schrödinger operators with singular potentials and magnetic fields. Zbl 1069.35064 Kolokol’tsov, V. N. 2 2003 Pricing of rainbow options: game theoretic approach. Zbl 1213.91154 Hucki, Z.; Kolokoltsov, V. N. 2 2007 Dynamic quantum games. Zbl 1494.91021 Kolokoltsov, Vassili N. 2 2022 Generalized mass action law and thermodynamics of nonlinear Markov processes. Zbl 1327.80015 Gorban, A. N.; Kolokoltsov, V. N. 1 2015 External pressure on alliances: what does the prisoners’ dilemma reveal? Zbl 1314.91153 Binner, Jane M.; Fletcher, Leslie R.; Kolokoltsov, Vassili; Ciardiello, Francesco 1 2013 On the asymptotics of low eigenvalues and eigenfunctions of the Schrödinger operator. Zbl 0828.35033 Kolokol’tsov, V. N. 1 1993 Asymptotically stable invariant tori of a vector field \(V(x)\) and the quasimodes of the operators \(V(x) \cdot \nabla- \varepsilon \Delta\). Zbl 0874.35101 Dobrokhotov, S. Yu.; Kolokol’tsov, V. N.; Martines Olive, Victor 1 1995 Stochastic monotonicity and duality of \(k\)th order with application to put-call symmetry of powered options. Zbl 1344.60074 Kolokoltsov, Vassili N. 1 2015 Introduction of a new Maslov-type currency (coupons) as a means of solving a market game under nonequilibrium prices. Zbl 0792.90012 Kolokol’tsov, V. N. 1 1991 The optimal assignment problem for a countable state space. Zbl 1179.90205 Akian, Marianne; Gaubert, Stéphane; Kolokoltsov, Vassili 1 2009 Stochastic integrals and SDE driven by nonlinear Lévy noise. Zbl 1227.60096 Kolokoltsov, Vassili N. 1 2011 Quasimodes of the diffusion operator \(-\varepsilon\Delta + v(x)\nabla\), corresponding to asymptotically stable limit cycles of the field \(v(x)\). Zbl 0874.35100 Dobrokhotov, Sergei Yu.; Kolokoltsov, Vassili N.; Olivé, Víctor M. 1 1994 The rate of escape of stable Ornstein-Uhlenbeck processes and the scattering theory for their perturbations. Zbl 0993.60088 Kolokol’tsov, V. N.; Tyukov, A. E. 1 2001 On the asymptotic behaviour of the kernel associated by a degenerated diffusion. (Sur le comportement asymptotique du noyau associé à une diffusion dégénérée.) Zbl 0970.35010 Albeverio, Sergio; Hilbert, Astrid; Kolokoltsov, Vassily 1 2000 Dynamic quantum games. Zbl 1494.91021 Kolokoltsov, Vassili N. 2 2022 Quantum mean-field games. Zbl 1498.91098 Kolokoltsov, Vassili N. 1 2022 Quantum mean-field games with the observations of counting type. Zbl 1478.91044 Kolokoltsov, Vassili N. 5 2021 Understanding game theory. Introduction to the analysis of many agent systems with competition and cooperation. 2nd edition. Zbl 1460.91005 Kolokoltsov, Vassili N.; Malafeyev, Oleg A. 4 2021 The law of large numbers for quantum stochastic filtering and control of many-particle systems. Zbl 1471.81056 Kolokoltsov, V. N. 3 2021 Monte Carlo estimation of the solution of fractional partial differential equations. Zbl 1488.65533 Kolokoltsov, Vassili; Lin, Feng; Mijatović, Aleksandar 1 2021 The probabilistic point of view on the generalized fractional partial differential equations. Zbl 1483.35002 Kolokoltsov, Vassili N. 21 2019 Many agent games in socio-economic systems: corruption, inspection, coalition building, network growth, security. Zbl 1431.91004 Kolokoltsov, Vassili N.; Malafeyev, Oleg A. 18 2019 Differential equations on measures and functional spaces. Zbl 1451.34001 Kolokoltsov, Vassili 18 2019 On mean field games with common noise and McKean-Vlasov SPDEs. Zbl 1415.60075 Kolokoltsov, Vassili N.; Troeva, Marianna 18 2019 Mixed fractional differential equations and generalized operator-valued Mittag-Leffler functions. Zbl 1439.35538 Kolokol’tsov, V. N. 4 2019 Regularity and sensitivity for McKean-Vlasov type SPDEs generated by stable-like processes. Zbl 1423.60101 Kolokoltsov, V. N.; Troeva, M. S. 5 2018 Corruption and botnet defense: a mean field game approach. Zbl 1417.91074 Kolokoltsov, V. N.; Malafeyev, O. A. 4 2018 Probabilistic solutions to nonlinear fractional differential equations of generalized Caputo and Riemann-Liouville type. Zbl 1498.60284 Hernández-Hernández, M. E.; Kolokoltsov, V. N. 3 2018 Mean-field-game model of corruption. Zbl 1391.91030 Kolokoltsov, V. N.; Malafeyev, O. A. 23 2017 Generalised fractional evolution equations of Caputo type. Zbl 1374.34009 Hernández-Hernández, M. E.; Kolokoltsov, V. N.; Toniazzi, L. 19 2017 The evolutionary game of pressure (or interference), resistance and collaboration. Zbl 1386.91028 Kolokoltsov, Vassili 9 2017 An approximate Nash equilibrium for pure jump Markov games of mean-field-type on continuous state space. Zbl 1395.91031 Basna, Rani; Hilbert, Astrid; Kolokoltsov, Vassili N. 6 2017 The fractional Hamilton-Jacobi-Bellman equation. Zbl 1365.60049 Veretennikova, M.; Kolokoltsov, V. 3 2017 Mean-field-game model for botnet defense in cyber-security. Zbl 1372.49049 Kolokoltsov, V. N.; Bensoussan, A. 18 2016 Evolutionary inspection and corruption games. Zbl 1406.91039 Katsikas, Stamatios; Kolokoltsov, Vassili; Yang, Wei 6 2016 On the probabilistic approach to the solution of generalized fractional differential equations of Caputo and Riemann-Liouville type. Zbl 1488.34038 Hernández-Hernández, M. E.; Kolokoltsov, V. N. 6 2016 On the solution of two-sided fractional ordinary differential equations of Caputo type. Zbl 1357.34014 Hernández-Hernández, Ma. Elena; Kolokoltsov, Vassili N. 5 2016 On fully mixed and multidimensional extensions of the Caputo and Riemann-Liouville derivatives, related Markov processes and fractional differential equations. Zbl 1321.26013 Kolokoltsov, Vassili 24 2015 Generalized mass action law and thermodynamics of nonlinear Markov processes. Zbl 1327.80015 Gorban, 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 1344.60074 Kolokoltsov, Vassili N. 1 2015 Well-posedness and regularity of the Cauchy problem for nonlinear fractional in time and space equations. Zbl 1412.35370 Kolokoltsov, V. N.; Veretennikova, M. A. 22 2014 On the rate of convergence for the mean-field approximation of controlled diffusions with large number of players. Zbl 1314.91020 Kolokoltsov, Vassili N.; Troeva, Marianna; Yang, Wei 18 2014 A fractional Hamilton Jacobi Bellman equation for scaled limits of controlled continuous time random walks. Zbl 1329.60117 Kolokoltsov, Vassili N.; Veretennikova, Maria A. 17 2014 The interval market model in mathematical finance. Game-theoretic methods. Zbl 1279.91005 Bernhard, Pierre; Engwerda, Jacob C.; Roorda, Berend; Schumacher, Johannes M.; Kolokoltsov, Vassili; Saint-Pierre, Patrick; Aubin, Jean-Pierre 16 2013 Stochastic duality of Markov processes: A study via generators. Zbl 1291.60154 Kolokoltsov, Vassili; Lee, Rui Xin 6 2013 Mean field games based on stable-like processes. Zbl 1287.91019 Kolokol’tsov, Vassiliĭ N.; Troeva, Marianna S.; Yang, Wei 3 2013 Nonlinear diffusions and stable-like processes with coefficients depending on the median or var. Zbl 1273.49031 Kolokoltsov, Vassili N. 3 2013 Nonlinear Lévy and nonlinear Feller processes: an analytic introduction. Zbl 1462.60066 Kolokoltsov, Vassili N. 3 2013 External pressure on alliances: what does the prisoners’ dilemma reveal? Zbl 1314.91153 Binner, Jane M.; Fletcher, Leslie R.; Kolokoltsov, Vassili; Ciardiello, Francesco 1 2013 Game theoretic analysis of incomplete markets: emergence of probabilities, nonlinear and fractional Black-Scholes equations. Zbl 1409.91239 Kolokoltsov, Vassili N. 1 2013 Turnpike theorems for Markov games. Zbl 1272.91027 Kolokoltsov, Vassili; Yang, Wei 14 2012 Uniform asymptotic bounds for the heat kernel and the trace of a stochastic geodesic flow. Zbl 1259.58012 Albeverio, Sergio; Hilbert, Astrid; Kolokoltsov, Vassily 3 2012 Markov processes, semigroups and generators. Zbl 1220.60003 Kolokoltsov, Vassili N. 104 2011 The Lévy-Khintchine type operators with variable Lipschitz continuous coefficients generate linear or nonlinear Markov processes and semigroups. Zbl 1235.60094 Kolokoltsov, Vassili N. 7 2011 Stochastic monotonicity and duality for one-dimensional Markov processes. Zbl 1237.60063 Kolokol’tsov, V. N. 6 2011 Stochastic integrals and SDE driven by nonlinear Lévy noise. Zbl 1227.60096 Kolokoltsov, Vassili N. 1 2011 Nonlinear Markov processes and kinetic equations. Zbl 1222.60003 Kolokoltsov, Vassili N. 123 2010 Understanding game theory. Introduction to the analysis of many agent systems with competition and cooperation. Zbl 1189.91001 Kolokoltsov, Vassili N.; Malafeyev, Oleg A. 9 2010 The central limit theorem for the Smoluchovski coagulation model. Zbl 1195.82057 Kolokoltsov, Vassili N. 3 2010 Generalized continuous-time random walks, subordination by hitting times, and fractional dynamics. Zbl 1193.60046 Kolokoltsov, V. N. 42 2009 The optimal assignment problem for a countable state space. Zbl 1179.90205 Akian, Marianne; Gaubert, Stéphane; Kolokoltsov, Vassili 1 2009 Nonlinear Markov semigroups and interacting Lévy type processes. Zbl 1110.82029 Kolokoltsov, Vassili N. 10 2007 Pricing of rainbow options: game theoretic approach. Zbl 1213.91154 Hucki, Z.; Kolokoltsov, V. N. 2 2007 Kinetic equations for the pure jump models of \(k\)-nary interacting particle systems. Zbl 1099.60072 Kolokoltsov, V. N. 7 2006 On the regularity of solutions to the spatially homogeneous Boltzmann equation with polynomially growing collision kernel. Zbl 1132.35338 Kolokoltsov, Vassili N. 3 2006 Fractionally stable distributions. Zbl 1201.76215 Bening, V. E.; Korolev, V. Yu.; Sukhorukova, T. A.; Gusarov, G. G.; Saenko, V. V.; Uchaikin, V. V.; Kolokoltsov, V. N. 2 2006 Set coverings and invertibility of functional Galois connections. Zbl 1080.06001 Akian, Marianne; Gaubert, Stéphane; Kolokoltsov, Vassili 14 2005 On Markov processes with decomposable pseudo-differential generators. Zbl 1091.60014 Kolokoltsov, Vassili N. 10 2004 Estimation of parameters of fractional stable distributions. Zbl 1130.62023 Bening, V. E.; Korolev, V. Yu.; Kolokol’tsov, V. N.; Saenko, V. V.; Uchaikin, V. V.; Zolotarev, V. M. 6 2004 Hydrodynamic limit of coagulation-fragmentation type models of \(k\)-nary interacting particles. Zbl 1157.82370 Kolokoltsov, Vassili N. 4 2004 Estimates for multiple stochastic integrals and stochastic Hamilton-Jacobi equations. Zbl 1060.70025 Kolokol’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 1080.60093 Kolokoltsov, Vassili N. 1 2004 On a general kinetic equation for many-particle systems with interaction, fragmentation and coagulation. Zbl 1070.82022 Belavkin, V. P.; Kolokol’tsov, V. N. 8 2003 Small time and semiclassical asymptotics for stochastic heat equations driven by Lévy noise. Zbl 1018.60062 Kolokol’tsov, V. N.; Tyukov, A. E. 4 2003 Measure-valued limits of interacting particle systems with \(k\)-nary interactions. I: One-dimensional limits. Zbl 1038.60094 Kolokoltsov, Vassili N. 4 2003 Schrödinger operators with singular potentials and magnetic fields. Zbl 1069.35064 Kolokol’tsov, V. N. 2 2003 On extensions of mollified Boltzmann and Smoluchowski equations to particle systems with a \(k\)-ary interaction. Zbl 1039.82029 Kolokoltsov, Vassili N. 1 2003 Invertibility of functional Galois connections. Zbl 1022.06001 Akian, Marianne; Gaubert, Stéphane; Kolokoltsov, Vassili 7 2002 Stochastic evolution as a quasiclassical limit of a boundary value problem for Schrödinger equations. Zbl 1057.60058 Belavkin, V. P.; Kolokol’tsov, V. N. 4 2002 Transience and non-explosion of certain stochastic Newtonian systems. Zbl 1013.60042 Kolokol’tsov, V. N.; Schilling, R. L.; Tyukov, A. E. 3 2002 A new path integral representation for the solutions of the Schrödinger, heat and stochastic Schrödinger equations. Zbl 1002.35104 Kolokoltsov, Vassili N. 2 2002 Fractional stable distributions. Zbl 0994.60010 Kolokoltsov, V.; Korolev, V.; Uchaikin, V. 11 2001 Idempotent structures in optimization. Zbl 1014.49019 Kolokol’tsov, V. N. 7 2001 Mathematics of the Feynman path integral. Zbl 1055.35054 Kolokoltsov, Vassili N. 2 2001 The rate of escape of stable Ornstein-Uhlenbeck processes and the scattering theory for their perturbations. Zbl 0993.60088 Kolokol’tsov, V. N.; Tyukov, A. E. 1 2001 Symmetric stable laws and stable-like jump-diffusions. Zbl 1021.60011 Kolokoltsov, Vassili 118 2000 Semiclassical analysis for diffusions and stochastic processes. Zbl 0951.60001 Kolokoltsov, V. N. 47 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 0970.35010 Albeverio, 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 0928.60061 Albeverio, Sergio; Hilbert, Astrid; Kolokoltsov, Vassili 5 1999 Idempotent structures in optimization. Zbl 0988.49015 Kolokoltsov, V. N. 1 1999 Nonexpansive maps and option pricing theory. Zbl 1274.91420 Kolokoltsov, Vassili N. 21 1998 Localization and analytic properties of the solutions of the simplest quantum filtering equation. Zbl 0927.60088 Kolokol’tsov, Vassili N. 7 1998 The stochastic HJB equation and WKB method. Zbl 0899.35128 Kolokoltsov, Vassili N. 1 1998 Idempotent analysis and its applications. Appendix by Pierre Del Moral. Transl. from the Russian by V. E. Nazaikinskij. Zbl 0941.93001 Kolokoltsov, V. N.; Maslov, V. P. 160 1997 Continuous quantum measurement: Local and global approaches. Zbl 0894.47058 Albeverio, S.; Kolokol’tsov, V. N.; Smolyanov, O. G. 7 1997 Transience of stochastically perturbed classical Hamiltonian systems and random wave operators. Zbl 0870.60052 Albeverio, S.; Hilbert, A.; Kolokoltsov, V. 3 1997 The rate of escape for some Gaussian processes and the scattering theory for their small perturbations. Zbl 0890.60051 Albeverio, Sergio; Kolokoltsov, Vassily N. 3 1997 A note on the long time asymptotics of the Brownian motion with application to the theory of quantum measurement. Zbl 0892.60086 Kolokoltsov, Vassili N. 3 1997 Asymptotic spectral analysis of a small diffusion operator and the life times of the corresponding diffusion process. Zbl 0912.58042 Kolokol’tsov, Vassili N.; Makarov, Konstantin A. 11 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 0857.60096 Albeverio, Sergio; Kolokol’tsov, Vassili N.; Smolyanov, Oleg G. 5 1996 Stochastic Hamiltonian-Jacobi-Bellman equation and stochastic Hamiltonian systems. Zbl 0967.60067 Kolokoltsov, V. N. 3 1996 Scattering theory for the Belavkin equation describing a quantum particle with continuously observed coordinate. Zbl 0845.35078 Kolokol’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 0820.60097 Dobrokhotov, Sergei Yu.; Kolokol’tsov, Vassili N. 8 1995 Asymptotically stable invariant tori of a vector field \(V(x)\) and the quasimodes of the operators \(V(x) \cdot \nabla- \varepsilon \Delta\). Zbl 0874.35101 Dobrokhotov, S. Yu.; Kolokol’tsov, V. N.; Martines Olive, Victor 1 1995 Long time behavior of the solutions of the Belavkin quantum filtering equation. Zbl 0942.81587 Kolokol’tsov, Vassili N. 1 1995 Idempotent analysis and its applications to optimal control. (Idempotentnyj analiz i ego primenenie v optimal’nom upravlenii.) Zbl 0857.49022 Maslov, V. P.; Kolokol’tsov, V. N. 29 1994 Quasimodes of the diffusion operator \(-\varepsilon\Delta + v(x)\nabla\), corresponding to asymptotically stable limit cycles of the field \(v(x)\). Zbl 0874.35100 Dobrokhotov, 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 0799.35050 Dobrokhotov, S. Yu.; Kolokol’tsov, V. N. 15 1993 On the asymptotics of low eigenvalues and eigenfunctions of the Schrödinger operator. Zbl 0828.35033 Kolokol’tsov, V. N. 1 1993 On linear, additive, and homogeneous operators in idempotent analysis. Zbl 0925.47016 Kolokoltsov, V. N. 11 1992 The stochastic Bellman equation as a nonlinear equation in Maslov spaces. Perturbation theory. Zbl 0802.49022 Kolokol’tsov, V. N. 5 1992 Quantization of the Bellman equation, exponential asymptotics and tunneling. Zbl 0796.35141 Dobrokhotov, S. Yu.; Kolokoltsov, V. N.; Maslov, V. P. 4 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 0745.35033 Dobrokhotov, S. Yu.; Kolokol’tsov, V. N.; Maslov, V. P. 18 1991 Introduction of a new Maslov-type currency (coupons) as a means of solving a market game under nonequilibrium prices. Zbl 0792.90012 Kolokol’tsov, V. N. 1 1991 ...and 8 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,120 Authors 46 Kolokoltsov, Vassili N. 26 Gaubert, Stéphane 22 Krivulin, Nikolai K. 14 Albeverio, Sergio A. 13 Chen, Zhen-Qing 12 Averboukh, Yuriĭ Vladimirovich 12 Menozzi, Stéphane 12 Pap, Endre 12 Schilling, René Leander 12 Smirnov, Sergeĭ Nikolaevich 11 Akian, Marianne 10 Maslov, Viktor Pavlovich 10 Sandrić, Nikola 9 Kühn, Franziska 9 Meerschaert, Mark Marvin 9 Štrboja, Mirjana 9 Wang, Jian 8 Bass, Richard F. 8 Liu, Junfeng 8 Matveev, Vladimir S. 8 McEneaney, William “Mac” M. 8 Ricciuti, Costantino 8 Wu, Jianglun 7 Agapov, Sergei Vadimovich 7 Kondrat’yev, Yuriĭ Grygorovych 7 Mazzucchi, Sonia 7 Mukhamedov, Farruh Maksutovich 7 Pavlyukevich, Ilya 7 Peperko, Aljoša 7 Sergeev, Sergeĭ Mikhaĭlovich 7 Toaldo, Bruno 7 Zaslavski, Alexander Yakovlevich 6 Anikin, Anatolii Yur’evich 6 Cavazos-Cadena, Rolando 6 Chaudru De Raynal, Paul-Eric 6 Embong, Ahmad Fadillah 6 Grbić, Tatjana 6 Katz, Ricardo David 6 Knopova, Victoria Pavlovna 6 Leonenko, Nikolai N. 6 Plavka, Ján 6 Pucacco, Giuseppe 6 Štajner-Papuga, Ivana 6 Troeva, Marianna S. 6 Wu, Ruoyu 5 Allamigeon, Xavier 5 Bäumer, Boris 5 Bolsinov, Alexey V. 5 Dobrokhotov, Sergei Yurievich 5 Kulik, Alexey M. 5 Mesiar, Radko 5 Mora, Carlos M. 5 Nguyen, Son Luu 5 Roquejoffre, Jean-Michel 5 Smolyanov, Oleg Georgievich 5 Yan, Litan 5 Zaitov, Adilbek Atakhanovich 4 Agahi, Hamzeh 4 Beghin, Luisa 4 Di Persio, Luca 4 Duan, Jinqiao 4 Fernandez, Arran 4 Fomenko, Anatoliĭ Timofeevich 4 Fujii, Masaaki 4 Hernández-Hernández, Daniel 4 Hilbert, Astrid 4 Klibanov, Michael V. 4 Kovács, Mihály 4 Kumagai, Takashi 4 Kutoviy, Oleksandr V. 4 Litvinov, Grigory Lazarevich 4 Mihailović, Biljana P. 4 Müller, Vladimír 4 Neumann, Berenice Anne 4 Orsingher, Enzo 4 Rosquist, Kjell 4 Saburov, Mansur Kh. 4 Sikorskii, Alla 4 Straka, Peter 4 Szpruch, Lukasz 4 Toniazzi, Lorenzo 4 Truman, Aubrey 4 Yin, George Gang 3 Ahmed, Yaqoub 3 Aida, Shigeki 3 Anh, Vo V. 3 Ascione, Giacomo 3 Aslam, Muhammad 3 Aubin, Jean-Pierre 3 Bayraktar, Erhan 3 Belomestny, Denis 3 Bennett, Jonathan 3 Bensoussan, Alain 3 Bernhard, Pierre 3 Butkovič, Peter 3 Camilli, Fabio 3 Clement, Emmanuelle 3 Di Nola, Antonio 3 Djehiche, Boualem 3 D’Ovidio, Mirko ...and 1,020 more Authors all top 5 Cited in 282 Serials 37 Stochastic Processes and their Applications 26 Mathematical Notes 26 Fractional Calculus & Applied Analysis 20 Linear Algebra and its Applications 19 Fuzzy Sets and Systems 18 Journal of Mathematical Sciences (New York) 17 Applied Mathematics and Optimization 16 Vestnik St. Petersburg University. 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