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## Kolokoltsov, Vassili N.

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 Author ID: kolokoltsov.vassili-n Published as: Kolokol’tsov, V. N.; Kolokol’tsov, Vassili N.; Kolokol’tsov, Vassiliĭ N.; Kolokoltsov, V.; Kolokoltsov, V. N.; Kolokoltsov, Vassili; Kolokoltsov, Vassili N.; Kolokoltsov, Vassily; Kolokoltsov, Vassily N.
 Documents Indexed: 118 Publications since 1982, including 11 Books
all top 5

#### Co-Authors

 52 single-authored 11 Maslov, Viktor Pavlovich 7 Albeverio, Sergio A. 6 Dobrokhotov, Sergei Yurievich 5 Hilbert, Astrid 5 Malafeev, Oleg Alekseivich 4 Korolev, Viktor Yur’evich 4 Troeva, Marianna S. 3 Akian, Marianne 3 Bening, Vladimir E. 3 Binner, Jane M. 3 Ciardiello, Francesco 3 Fletcher, Leslie R. 3 Gaubert, Stéphane 3 Tyukov, Alexey E. 3 Uchaĭkin, Vladimir Vasil’evich 3 Veretennikova, Maria A. 2 Belavkin, Viacheslav 2 Hernández-Hernández, Ma. Elena 2 Saenko, Viacheslav V. 2 Schilling, René Leander 2 Smolyanov, Oleg Georgievich 2 Tyukov, Alexei E. 2 Yang, Wei 1 Aubin, Jean-Pierre 1 Ball, Robin C. 1 Basna, Rani 1 Bensoussan, Alain 1 Bernhard, Pierre 1 Cecchin, Alekos 1 Engwerda, Jacob Christiaan 1 Gorban, Alexander N. 1 Gusarov, G. G. 1 Hucki, Z. 1 Katsikas, Stamatios 1 Lebedev, Dimitri R. 1 Lee, Rui Xin 1 Lin, Feng 1 MacKay, Robert Sinclair 1 Makarov, Konstantin A. 1 Martines Olive, Victor 1 Mijatović, Aleksandar 1 Olivé, Victor M. 1 Roorda, Berend 1 Saint-Pierre, Patrick 1 Schumacher, Johannes M. 1 Sukhorukova, T. A. 1 Toniazzi, Lorenzo 1 Yang, Wei 1 Yang, Wei 1 Zolotarëv, Vladimir Mikhaĭlovich
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#### Serials

 4 Mathematical Notes 4 Stochastics and Stochastics Reports 4 Journal of Mathematical Sciences (New York) 4 Fractional Calculus & Applied Analysis 3 Soviet Mathematics. Doklady 3 Probability Theory and Related Fields 3 Russian Academy of Sciences. Doklady. Mathematics 3 Dynamic Games and Applications 2 Journal of Mathematical Physics 2 Journal of Statistical Physics 2 Matematicheskie Zametki 2 Theoretical and Mathematical Physics 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 Stochastics 2 Games 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Moscow University Mathematics Bulletin 1 Russian Mathematical Surveys 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 Comptes Rendus Mathématiques de l’Académie des Sciences 1 Revista Matemática Iberoamericana 1 Journal of Theoretical 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 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 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
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#### Fields

 55 Probability theory and stochastic processes (60-XX) 32 Partial differential equations (35-XX) 28 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 21 Calculus of variations and optimal control; optimization (49-XX) 21 Quantum theory (81-XX) 14 Statistical mechanics, structure of matter (82-XX) 11 Operations research, mathematical programming (90-XX) 10 Operator theory (47-XX) 8 Ordinary differential equations (34-XX) 6 Real functions (26-XX) 6 Global analysis, analysis on manifolds (58-XX) 6 Systems theory; control (93-XX) 5 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 Integral transforms, operational calculus (44-XX) 2 Statistics (62-XX) 2 Fluid mechanics (76-XX) 1 General and overarching topics; collections (00-XX) 1 Associative rings and algebras (16-XX) 1 Group theory and generalizations (20-XX) 1 Measure and integration (28-XX) 1 Special functions (33-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 Information and communication theory, circuits (94-XX)

#### Citations contained in zbMATH Open

87 Publications have been cited 751 times in 564 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.
1997
Symmetric stable laws and stable-like jump-diffusions. Zbl 1021.60011
Kolokoltsov, Vassili
2000
Markov processes, semigroups and generators. Zbl 1220.60003
Kolokoltsov, Vassili N.
2011
Nonlinear Markov processes and kinetic equations. Zbl 1222.60003
Kolokoltsov, Vassili N.
2010
Semiclassical analysis for diffusions and stochastic processes. Zbl 0951.60001
Kolokoltsov, V. N.
2000
Generalized continuous-time random walks, subordination by hitting times, and fractional dynamics. Zbl 1193.60046
Kolokoltsov, V. N.
2009
Geodesic flows on two-dimensional manifolds with an additional first integral that is polynomial in the velocities. Zbl 0548.58028
Kolokol’tsov, V. N.
1983
Nonexpansive maps and option pricing theory. Zbl 1274.91420
Kolokoltsov, Vassili N.
1998
Idempotent analysis as a tool of control theory and optimal synthesis. I. Zbl 0709.49014
Kolokol’tsov, V. N.; Maslov, V. P.
1989
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
2014
Turnpike theorems for Markov games. Zbl 1272.91027
Kolokoltsov, Vassili; Yang, Wei
2012
Set coverings and invertibility of functional Galois connections. Zbl 1080.06001
Akian, Marianne; Gaubert, Stéphane; Kolokoltsov, Vassili
2005
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.
1991
Geodesic flows on two-dimensional manifolds with according to the velocities complementary polynomial first integral. Zbl 0518.58033
Kolokol’tsov, V. N.
1982
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
2015
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.
1996
Scattering theory for the Belavkin equation describing a quantum particle with continuously observed coordinate. Zbl 0845.35078
Kolokol’tsov, Vassili N.
1995
On linear, additive, and homogeneous operators in idempotent analysis. Zbl 0925.47016
Kolokoltsov, V. N.
1992
Generalised fractional evolution equations of Caputo type. Zbl 1374.34009
Hernández-Hernández, M. E.; Kolokoltsov, V. N.; Toniazzi, L.
2017
Mean-field-game model of corruption. Zbl 1391.91030
Kolokoltsov, V. N.; Malafeyev, O. A.
2017
On Markov processes with decomposable pseudo-differential generators. Zbl 1091.60014
Kolokoltsov, Vassili N.
2004
On mean field games with common noise and McKean-Vlasov SPDEs. Zbl 1415.60075
Kolokoltsov, Vassili N.; Troeva, Marianna
2019
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.
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.
2014
Nonlinear Markov semigroups and interacting Lévy type processes. Zbl 1110.82029
Kolokoltsov, Vassili N.
2007
Fractional stable distributions. Zbl 0994.60010
Kolokoltsov, V.; Korolev, V.; Uchaikin, V.
2001
Idempotent analysis and its applications to optimal control. Zbl 0857.49022
Maslov, V. P.; Kolokol’tsov, V. N.
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.
1993
The evolutionary game of pressure (or interference), resistance and collaboration. Zbl 1386.91028
Kolokoltsov, Vassili
2017
Stochastic duality of Markov processes: A study via generators. Zbl 1291.60154
Kolokoltsov, Vassili; Lee, Rui Xin
2013
Localization and analytic properties of the solutions of the simplest quantum filtering equation. Zbl 0927.60088
Kolokol’tsov, Vassili N.
1998
Continuous quantum measurement: Local and global approaches. Zbl 0894.47058
Albeverio, S.; Kolokol’tsov, V. N.; Smolyanov, O. G.
1997
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.
1995
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
2013
Kinetic equations for the pure jump models of $$k$$-nary interacting particle systems. Zbl 1099.60072
Kolokoltsov, V. N.
2006
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
1999
The probabilistic point of view on the generalized fractional partial differential equations. Zbl 07115448
Kolokoltsov, Vassili N.
2019
Mean-field-game model for botnet defense in cyber-security. Zbl 1372.49049
Kolokoltsov, V. N.; Bensoussan, A.
2016
On the solution of two-sided fractional ordinary differential equations of Caputo type. Zbl 1357.34014
Hernández-Hernández, Ma. Elena; Kolokoltsov, Vassili N.
2016
Stochastic monotonicity and duality for one-dimensional Markov processes. Zbl 1237.60063
Kolokol’tsov, V. N.
2011
Understanding game theory. Introduction to the analysis of many agent systems with competition and cooperation. Zbl 1189.91001
Kolokoltsov, Vassili N.; Malafeyev, Oleg A.
2010
Hydrodynamic limit of coagulation-fragmentation type models of $$k$$-nary interacting particles. Zbl 1157.82370
Kolokoltsov, Vassili N.
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.
2004
Measure-valued limits of interacting particle systems with $$k$$-nary interactions. I: One-dimensional limits. Zbl 1038.60094
Kolokoltsov, Vassili N.
2003
Small time and semiclassical asymptotics for stochastic heat equations driven by Lévy noise. Zbl 1018.60062
Kolokol’tsov, V. N.; Tyukov, A. E.
2003
Invertibility of functional Galois connections. Zbl 1022.06001
Akian, Marianne; Gaubert, Stéphane; Kolokoltsov, Vassili
2002
Transience of stochastically perturbed classical Hamiltonian systems and random wave operators. Zbl 0870.60052
Albeverio, S.; Hilbert, A.; Kolokoltsov, V.
1997
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.
1988
The fractional Hamilton-Jacobi-Bellman equation. Zbl 1365.60049
Veretennikova, M.; Kolokoltsov, V.
2017
On the regularity of solutions to the spatially homogeneous Boltzmann equation with polynomially growing collision kernel. Zbl 1132.35338
Kolokoltsov, Vassili N.
2006
On a general kinetic equation for many-particle systems with interaction, fragmentation and coagulation. Zbl 1070.82022
Belavkin, V. P.; Kolokol’tsov, V. N.
2003
Idempotent structures in optimization. Zbl 1014.49019
Kolokol’tsov, V. N.
2001
The rate of escape for some Gaussian processes and the scattering theory for their small perturbations. Zbl 0890.60051
Albeverio, Sergio; Kolokoltsov, Vassily N.
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.
1997
Stochastic Hamiltonian-Jacobi-Bellman equation and stochastic Hamiltonian systems. Zbl 0967.60067
Kolokoltsov, V. N.
1996
Quantization of the Bellman equation, exponential asymptotics and tunneling. Zbl 0796.35141
Dobrokhotov, S. Yu.; Kolokoltsov, V. N.; Maslov, V. P.
1992
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.
2017
Evolutionary inspection and corruption games. Zbl 1406.91039
Katsikas, Stamatios; Kolokoltsov, Vassili; Yang, Wei
2016
Nonlinear diffusions and stable-like processes with coefficients depending on the median or var. Zbl 1273.49031
Kolokoltsov, Vassili N.
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
2012
The Lévy-Khintchine type operators with variable Lipschitz continuous coefficients generate linear or nonlinear Markov processes and semigroups. Zbl 1235.60094
Kolokoltsov, Vassili N.
2011
The central limit theorem for the Smoluchovski coagulation model. Zbl 1195.82057
Kolokoltsov, Vassili N.
2010
Estimates for multiple stochastic integrals and stochastic Hamilton-Jacobi equations. Zbl 1060.70025
Kolokol’tsov, Vassili N.; Schilling, René L.; Tyukov, Alexei E.
2004
Transience and non-explosion of certain stochastic Newtonian systems. Zbl 1013.60042
Kolokol’tsov, V. N.; Schilling, R. L.; Tyukov, A. E.
2002
A new path integral representation for the solutions of the Schrödinger, heat and stochastic Schrödinger equations. Zbl 1002.35104
Kolokoltsov, Vassili N.
2002
Mathematics of the Feynman path integral. Zbl 1055.35054
Kolokoltsov, Vassili N.
2001
The Cauchy problem for the homogeneous Bellman equation. Zbl 0666.35018
Kolokol’tsov, V. N.; Maslov, V. P.
1988
Mixed fractional differential equations and generalized operator-valued Mittag-Leffler functions. Zbl 1439.35538
Kolokol’tsov, V. N.
2019
Many agent games in socio-economic systems: corruption, inspection, coalition building, network growth, security. Zbl 1431.91004
Kolokoltsov, Vassili N.; Malafeyev, Oleg A.
2019
Stochastic monotonicity and duality of $$k$$th order with application to put-call symmetry of powered options. Zbl 1344.60074
Kolokoltsov, Vassili N.
2015
External pressure on alliances: what does the prisoners’ dilemma reveal? Zbl 1314.91153
Binner, Jane M.; Fletcher, Leslie R.; Kolokoltsov, Vassili; Ciardiello, Francesco
2013
Mean field games based on stable-like processes. Zbl 1287.91019
Kolokol’tsov, Vassiliĭ N.; Troeva, Marianna S.; Yang, Wei
2013
Stochastic integrals and SDE driven by nonlinear Lévy noise. Zbl 1227.60096
Kolokoltsov, Vassili N.
2011
The optimal assignment problem for a countable state space. Zbl 1179.90205
Akian, Marianne; Gaubert, Stéphane; Kolokoltsov, Vassili
2009
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.
2006
Measure-valued limits of interacting particle systems with $$k$$-nary interactions. II. Finite-dimensional limits. Zbl 1080.60093
Kolokoltsov, Vassili N.
2004
Schrödinger operators with singular potentials and magnetic fields. Zbl 1069.35064
Kolokol’tsov, V. N.
2003
On extensions of mollified Boltzmann and Smoluchowski equations to particle systems with a $$k$$-ary interaction. Zbl 1039.82029
Kolokoltsov, Vassili N.
2003
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.
2001
On the asymptotic behaviour of the kernel associated by a degenerated diffusion. Zbl 0970.35010
Albeverio, Sergio; Hilbert, Astrid; Kolokoltsov, Vassily
2000
The stochastic HJB equation and WKB method. Zbl 0899.35128
Kolokoltsov, Vassili N.
1998
Representation of the solutions of the Belavkin quantum measurement equation by a rigorous version of the Menski functional integration formula. Zbl 0857.60096
Albeverio, Sergio; Kolokol’tsov, Vassili N.; Smolyanov, Oleg G.
1996
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
1995
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.
1994
Idempotent analysis as a tool of control theory and optimal synthesis. II. Zbl 0709.49015
Kolokol’tsov, V. N.; Maslov, V. P.
1989
Turnpikes and infinite extremals in Markov decision processes. Zbl 0692.90102
Kolokol’tsov, V. N.
1989
Idempotent analysis as a tool of control theory and optimal synthesis. I. Zbl 0692.49022
Kolokol’tsov, V. N.; Maslov, V. P.
1989
On mean field games with common noise and McKean-Vlasov SPDEs. Zbl 1415.60075
Kolokoltsov, Vassili N.; Troeva, Marianna
2019
The probabilistic point of view on the generalized fractional partial differential equations. Zbl 07115448
Kolokoltsov, Vassili N.
2019
Mixed fractional differential equations and generalized operator-valued Mittag-Leffler functions. Zbl 1439.35538
Kolokol’tsov, V. N.
2019
Many agent games in socio-economic systems: corruption, inspection, coalition building, network growth, security. Zbl 1431.91004
Kolokoltsov, Vassili N.; Malafeyev, Oleg A.
2019
Generalised fractional evolution equations of Caputo type. Zbl 1374.34009
Hernández-Hernández, M. E.; Kolokoltsov, V. N.; Toniazzi, L.
2017
Mean-field-game model of corruption. Zbl 1391.91030
Kolokoltsov, V. N.; Malafeyev, O. A.
2017
The evolutionary game of pressure (or interference), resistance and collaboration. Zbl 1386.91028
Kolokoltsov, Vassili
2017
The fractional Hamilton-Jacobi-Bellman equation. Zbl 1365.60049
Veretennikova, M.; Kolokoltsov, V.
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.
2017
Mean-field-game model for botnet defense in cyber-security. Zbl 1372.49049
Kolokoltsov, V. N.; Bensoussan, A.
2016
On the solution of two-sided fractional ordinary differential equations of Caputo type. Zbl 1357.34014
Hernández-Hernández, Ma. Elena; Kolokoltsov, Vassili N.
2016
Evolutionary inspection and corruption games. Zbl 1406.91039
Katsikas, Stamatios; Kolokoltsov, Vassili; Yang, Wei
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
2015
Stochastic monotonicity and duality of $$k$$th order with application to put-call symmetry of powered options. Zbl 1344.60074
Kolokoltsov, Vassili N.
2015
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
2014
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.
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.
2014
Stochastic duality of Markov processes: A study via generators. Zbl 1291.60154
Kolokoltsov, Vassili; Lee, Rui Xin
2013
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
2013
Nonlinear diffusions and stable-like processes with coefficients depending on the median or var. Zbl 1273.49031
Kolokoltsov, Vassili N.
2013
External pressure on alliances: what does the prisoners’ dilemma reveal? Zbl 1314.91153
Binner, Jane M.; Fletcher, Leslie R.; Kolokoltsov, Vassili; Ciardiello, Francesco
2013
Mean field games based on stable-like processes. Zbl 1287.91019
Kolokol’tsov, Vassiliĭ N.; Troeva, Marianna S.; Yang, Wei
2013
Turnpike theorems for Markov games. Zbl 1272.91027
Kolokoltsov, Vassili; Yang, Wei
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
2012
Markov processes, semigroups and generators. Zbl 1220.60003
Kolokoltsov, Vassili N.
2011
Stochastic monotonicity and duality for one-dimensional Markov processes. Zbl 1237.60063
Kolokol’tsov, V. N.
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.
2011
Stochastic integrals and SDE driven by nonlinear Lévy noise. Zbl 1227.60096
Kolokoltsov, Vassili N.
2011
Nonlinear Markov processes and kinetic equations. Zbl 1222.60003
Kolokoltsov, Vassili N.
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.
2010
The central limit theorem for the Smoluchovski coagulation model. Zbl 1195.82057
Kolokoltsov, Vassili N.
2010
Generalized continuous-time random walks, subordination by hitting times, and fractional dynamics. Zbl 1193.60046
Kolokoltsov, V. N.
2009
The optimal assignment problem for a countable state space. Zbl 1179.90205
Akian, Marianne; Gaubert, Stéphane; Kolokoltsov, Vassili
2009
Nonlinear Markov semigroups and interacting Lévy type processes. Zbl 1110.82029
Kolokoltsov, Vassili N.
2007
Kinetic equations for the pure jump models of $$k$$-nary interacting particle systems. Zbl 1099.60072
Kolokoltsov, V. N.
2006
On the regularity of solutions to the spatially homogeneous Boltzmann equation with polynomially growing collision kernel. Zbl 1132.35338
Kolokoltsov, Vassili N.
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.
2006
Set coverings and invertibility of functional Galois connections. Zbl 1080.06001
Akian, Marianne; Gaubert, Stéphane; Kolokoltsov, Vassili
2005
On Markov processes with decomposable pseudo-differential generators. Zbl 1091.60014
Kolokoltsov, Vassili N.
2004
Hydrodynamic limit of coagulation-fragmentation type models of $$k$$-nary interacting particles. Zbl 1157.82370
Kolokoltsov, Vassili N.
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.
2004
Estimates for multiple stochastic integrals and stochastic Hamilton-Jacobi equations. Zbl 1060.70025
Kolokol’tsov, Vassili N.; Schilling, René L.; Tyukov, Alexei E.
2004
Measure-valued limits of interacting particle systems with $$k$$-nary interactions. II. Finite-dimensional limits. Zbl 1080.60093
Kolokoltsov, Vassili N.
2004
Measure-valued limits of interacting particle systems with $$k$$-nary interactions. I: One-dimensional limits. Zbl 1038.60094
Kolokoltsov, Vassili N.
2003
Small time and semiclassical asymptotics for stochastic heat equations driven by Lévy noise. Zbl 1018.60062
Kolokol’tsov, V. N.; Tyukov, A. E.
2003
On a general kinetic equation for many-particle systems with interaction, fragmentation and coagulation. Zbl 1070.82022
Belavkin, V. P.; Kolokol’tsov, V. N.
2003
Schrödinger operators with singular potentials and magnetic fields. Zbl 1069.35064
Kolokol’tsov, V. N.
2003
On extensions of mollified Boltzmann and Smoluchowski equations to particle systems with a $$k$$-ary interaction. Zbl 1039.82029
Kolokoltsov, Vassili N.
2003
Invertibility of functional Galois connections. Zbl 1022.06001
Akian, Marianne; Gaubert, Stéphane; Kolokoltsov, Vassili
2002
Transience and non-explosion of certain stochastic Newtonian systems. Zbl 1013.60042
Kolokol’tsov, V. N.; Schilling, R. L.; Tyukov, A. E.
2002
A new path integral representation for the solutions of the Schrödinger, heat and stochastic Schrödinger equations. Zbl 1002.35104
Kolokoltsov, Vassili N.
2002
Fractional stable distributions. Zbl 0994.60010
Kolokoltsov, V.; Korolev, V.; Uchaikin, V.
2001
Idempotent structures in optimization. Zbl 1014.49019
Kolokol’tsov, V. N.
2001
Mathematics of the Feynman path integral. Zbl 1055.35054
Kolokoltsov, Vassili N.
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.
2001
Symmetric stable laws and stable-like jump-diffusions. Zbl 1021.60011
Kolokoltsov, Vassili
2000
Semiclassical analysis for diffusions and stochastic processes. Zbl 0951.60001
Kolokoltsov, V. N.
2000
On the asymptotic behaviour of the kernel associated by a degenerated diffusion. Zbl 0970.35010
Albeverio, Sergio; Hilbert, Astrid; Kolokoltsov, Vassily
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
1999
Nonexpansive maps and option pricing theory. Zbl 1274.91420
Kolokoltsov, Vassili N.
1998
Localization and analytic properties of the solutions of the simplest quantum filtering equation. Zbl 0927.60088
Kolokol’tsov, Vassili N.
1998
The stochastic HJB equation and WKB method. Zbl 0899.35128
Kolokoltsov, Vassili N.
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.
1997
Continuous quantum measurement: Local and global approaches. Zbl 0894.47058
Albeverio, S.; Kolokol’tsov, V. N.; Smolyanov, O. G.
1997
Transience of stochastically perturbed classical Hamiltonian systems and random wave operators. Zbl 0870.60052
Albeverio, S.; Hilbert, A.; Kolokoltsov, V.
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.
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.
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.
1996
Stochastic Hamiltonian-Jacobi-Bellman equation and stochastic Hamiltonian systems. Zbl 0967.60067
Kolokoltsov, V. N.
1996
Representation of the solutions of the Belavkin quantum measurement equation by a rigorous version of the Menski functional integration formula. Zbl 0857.60096
Albeverio, Sergio; Kolokol’tsov, Vassili N.; Smolyanov, Oleg G.
1996
Scattering theory for the Belavkin equation describing a quantum particle with continuously observed coordinate. Zbl 0845.35078
Kolokol’tsov, Vassili N.
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.
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
1995
Idempotent analysis and its applications to optimal control. Zbl 0857.49022
Maslov, V. P.; Kolokol’tsov, V. N.
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.
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.
1993
On linear, additive, and homogeneous operators in idempotent analysis. Zbl 0925.47016
Kolokoltsov, V. N.
1992
Quantization of the Bellman equation, exponential asymptotics and tunneling. Zbl 0796.35141
Dobrokhotov, S. Yu.; Kolokoltsov, V. N.; Maslov, V. P.
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.
1991
Idempotent analysis as a tool of control theory and optimal synthesis. I. Zbl 0709.49014
Kolokol’tsov, V. N.; Maslov, V. P.
1989
Idempotent analysis as a tool of control theory and optimal synthesis. II. Zbl 0709.49015
Kolokol’tsov, V. N.; Maslov, V. P.
1989
Turnpikes and infinite extremals in Markov decision processes. Zbl 0692.90102
Kolokol’tsov, V. N.
1989
Idempotent analysis as a tool of control theory and optimal synthesis. I. Zbl 0692.49022
Kolokol’tsov, V. N.; Maslov, V. P.
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 0655.46020
Kolokol’tsov, V. N.; Maslov, V. P.
1988
The Cauchy problem for the homogeneous Bellman equation. Zbl 0666.35018
Kolokol’tsov, V. N.; Maslov, V. P.
1988
Geodesic flows on two-dimensional manifolds with an additional first integral that is polynomial in the velocities. Zbl 0548.58028
Kolokol’tsov, V. N.
1983
Geodesic flows on two-dimensional manifolds with according to the velocities complementary polynomial first integral. Zbl 0518.58033
Kolokol’tsov, V. N.
1982
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#### Cited by 687 Authors

 35 Kolokoltsov, Vassili N. 23 Gaubert, Stéphane 13 Albeverio, Sergio A. 13 Chen, Zhen-Qing 10 Pap, Endre 10 Schilling, René Leander 9 Akian, Marianne 9 Meerschaert, Mark M. 8 Bass, Richard F. 8 Krivulin, Nikolai K. 8 Maslov, Viktor Pavlovich 8 Wang, Jian 7 McEneaney, William M. 7 Menozzi, Stéphane 7 Sandrić, Nikola 7 Sergeev, Sergeĭ Mikhaĭlovich 7 Štrboja, Mirjana 7 Zaslavski, Alexander Yakovlevich 6 Averboukh, Yuriĭ Vladimirovich 6 Katz, Ricardo David 6 Liu, Junfeng 6 Matveev, Vladimir S. 6 Pavlyukevich, Ilya 6 Ricciuti, Costantino 6 Saburov, Mansoor 6 Štajner-Papuga, Ivana 6 Wu, Jianglun 5 Allamigeon, Xavier 5 Bäumer, Boris 5 Bolsinov, Alexey V. 5 Cavazos-Cadena, Rolando 5 Grbić, Tatjana 5 Knopova, Victoria Pavlovna 5 Kondrat’yev, Yuriĭ Grygorovych 5 Peperko, Aljoša 5 Toaldo, Bruno 5 Yan, Litan 4 Anikin, A. Yu. 4 Dobrokhotov, Sergei Yurievich 4 Kovács, Mihály 4 Kühn, Franziska 4 Kumagai, Takashi 4 Kutoviy, Oleksandr V. 4 Leonenko, Nikolai N. 4 Mazzucchi, Sonia 4 Mesiar, Radko 4 Orsingher, Enzo 4 Pucacco, Giuseppe 4 Roquejoffre, Jean-Michel 4 Sikorskii, Alla 4 Straka, Peter 3 Agahi, Hamzeh 3 Aida, Shigeki 3 Anh, Vo V. 3 Beghin, Luisa 3 Bennett, Jonathan 3 Bensoussan, Alain 3 Butkovič, Peter 3 Clement, Emmanuelle 3 Di Nola, Antonio 3 Finkelshteĭn, Dmitriĭ Leonidovich 3 Fomenko, Anatoliĭ Timofeevich 3 Foondun, Mohammud 3 Gomes, Diogo Luís Aguiar 3 Hernández-Hernández, Daniel 3 Hochart, Antoine 3 Kassmann, Moritz 3 Kim, Panki 3 Kochubeĭ, Anatoliĭ Naumovych 3 Konakov, Valentin 3 Litvinov, Grigory Lazarevich 3 Liu, Jianguo 3 Mora, Carlos M. 3 Müller, Vladimír 3 Papić, I. 3 Priola, Enrico 3 Pułka, Małgorzata 3 Rosquist, Kjell 3 Saburov, Mansur Kh. 3 Sankaranarayanan, Harish 3 Schneider, Hans 3 Smii, Boubaker 3 Šuvak, Nenad 3 Toniazzi, Lorenzo 3 Troeva, Marianna S. 3 Truman, Aubrey 3 Vybornyi, E. V. 3 Wang, Jieming 2 Agapov, Sergei Vadimovich 2 Bacaër, Nicolas 2 Bally, Vlad 2 Bartoszek, Krzysztof 2 Bassi, Angelo 2 Belavkin, Viacheslav 2 Belomestny, Denis 2 Bening, Vladimir E. 2 Bernhard, Pierre 2 Bialy, Misha 2 Biswas, Anup 2 Budhiraja, Amarjit S. ...and 587 more Authors
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#### Cited in 197 Serials

 25 Stochastic Processes and their Applications 18 Linear Algebra and its Applications 17 Mathematical Notes 15 Fractional Calculus & Applied Analysis 13 Fuzzy Sets and Systems 11 Journal of Functional Analysis 11 Transactions of the American Mathematical Society 11 Journal of Theoretical Probability 11 Journal of Mathematical Sciences (New York) 10 Journal of Mathematical Analysis and Applications 10 Applied Mathematics and Optimization 10 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 10 Dynamic Games and Applications 9 Journal of Differential Equations 9 Bernoulli 8 Journal of Mathematical Physics 8 Journal of Statistical Physics 8 Theoretical and Mathematical Physics 8 Stochastic Analysis and Applications 8 Probability Theory and Related Fields 8 Infinite Dimensional Analysis, Quantum Probability and Related Topics 7 Journal of Geometry and Physics 7 The Annals of Applied Probability 7 Russian Journal of Mathematical Physics 6 Reviews in Mathematical Physics 6 SIAM Journal on Control and Optimization 6 Discrete and Continuous Dynamical Systems 5 Computers & Mathematics with Applications 5 Kybernetika 5 Vestnik St. Petersburg University. Mathematics 5 Electronic Journal of Probability 4 The Annals of Probability 4 Applied Mathematics and Computation 4 Information Sciences 4 Journal of Computational and Applied Mathematics 4 Communications in Partial Differential Equations 4 Potential Analysis 4 NoDEA. Nonlinear Differential Equations and Applications 4 European Series in Applied and Industrial Mathematics (ESAIM): Probability and Statistics 4 Stochastics and Dynamics 4 Journal of Dynamics and Games 3 Communications in Mathematical Physics 3 Journal of Computational Physics 3 Moscow University Mathematics Bulletin 3 Chaos, Solitons and Fractals 3 Automatica 3 Functional Analysis and its Applications 3 Osaka Journal of Mathematics 3 Proceedings of the American Mathematical Society 3 Theoretical Computer Science 3 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 3 Journal de Mathématiques Pures et Appliquées. Neuvième Série 3 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 3 Journal of Nonlinear Science 3 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 3 Chaos 3 Proceedings of the Steklov Institute of Mathematics 3 Set-Valued and Variational Analysis 3 Games 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 Results in Mathematics 2 Semigroup Forum 2 Siberian Mathematical Journal 2 International Journal of Approximate Reasoning 2 Discrete Event Dynamic Systems 2 Mathematical Problems in Engineering 2 Finance and Stochastics 2 Doklady Mathematics 2 Differential Equations 2 Journal of Evolution Equations 2 Dynamics of Continuous, Discrete & Impulsive Systems. Series B. Applications & Algorithms 2 Discrete and Continuous Dynamical Systems. Series B 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Vladikavkazskiĭ Matematicheskiĭ Zhurnal 2 Stochastics 2 ALEA. Latin American Journal of Probability and Mathematical Statistics 2 Frontiers of Mathematics in China 2 Matematicheskaya Teoriya Igr i eë Prilozheniya 2 Journal of Applied Analysis and Computation 2 Journal of Logical and Algebraic Methods in Programming 2 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings and Surveys 1 International Journal of Modern Physics B 1 Applicable Analysis 1 Artificial Intelligence 1 Archive for Rational Mechanics and Analysis 1 Indian Journal of Pure & Applied Mathematics 1 Letters in Mathematical Physics 1 Nonlinearity 1 Physica A 1 Physics Letters. A 1 Reports on Mathematical Physics 1 Theory of Probability and its Applications 1 Acta Mathematica Vietnamica ...and 97 more Serials
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#### Cited in 55 Fields

 255 Probability theory and stochastic processes (60-XX) 138 Partial differential equations (35-XX) 73 Operator theory (47-XX) 69 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 48 Calculus of variations and optimal control; optimization (49-XX) 44 Statistical mechanics, structure of matter (82-XX) 42 Systems theory; control (93-XX) 37 Quantum theory (81-XX) 33 Dynamical systems and ergodic theory (37-XX) 32 Real functions (26-XX) 30 Linear and multilinear algebra; matrix theory (15-XX) 30 Numerical analysis (65-XX) 26 Operations research, mathematical programming (90-XX) 25 Differential geometry (53-XX) 24 Measure and integration (28-XX) 23 Ordinary differential equations (34-XX) 21 Associative rings and algebras (16-XX) 17 Global analysis, analysis on manifolds (58-XX) 17 Statistics (62-XX) 16 Functional analysis (46-XX) 14 Computer science (68-XX) 13 Mechanics of particles and systems (70-XX) 12 Order, lattices, ordered algebraic structures (06-XX) 11 Algebraic geometry (14-XX) 10 Fluid mechanics (76-XX) 10 Biology and other natural sciences (92-XX) 9 Integral equations (45-XX) 9 Convex and discrete geometry (52-XX) 8 Combinatorics (05-XX) 8 General topology (54-XX) 7 Number theory (11-XX) 7 Potential theory (31-XX) 5 Category theory; homological algebra (18-XX) 5 Approximations and expansions (41-XX) 4 Mathematical logic and foundations (03-XX) 4 Field theory and polynomials (12-XX) 4 Special functions (33-XX) 4 Manifolds and cell complexes (57-XX) 3 General algebraic systems (08-XX) 3 Group theory and generalizations (20-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 2 Commutative algebra (13-XX) 2 Nonassociative rings and algebras (17-XX) 2 Difference and functional equations (39-XX) 2 Optics, electromagnetic theory (78-XX) 2 Classical thermodynamics, heat transfer (80-XX) 2 Information and communication theory, circuits (94-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Topological groups, Lie groups (22-XX) 1 Functions of a complex variable (30-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Sequences, series, summability (40-XX) 1 Integral transforms, operational calculus (44-XX) 1 Geometry (51-XX)