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Journal Article
Kolokoltsov, Vassili N. (2023) On the control over the distribution of ticks based on the extensions of the KISS model. Mathematics, 11 (2). 478. doi:10.3390/math11020478 ISSN 2227-7390.
Kolokoltsov, Vassili N. (2022) Quantum mean-field games. The Annals of Applied Probability, 32 (3). pp. 2254-2288. doi:10.1214/21-aap1733 ISSN 1050-5164.
Kolokoltsov, Vassili N. (2022) Dynamic quantum games. Dynamic Games and Applications, 12 . pp. 552-573. doi:10.1007/s13235-021-00389-w ISSN 2153-0785.
Kolokoltsov, Vassili N. (2022) On a probabilistic derivation of the basic particle statistics (Bose–Einstein, Fermi–Dirac, canonical, grand-canonical, intermediate) and related distributions. Transactions of the Moscow Mathematical Society, 82 . pp. 77-87. doi:10.1090/mosc/316 ISSN 0077-1554.
Kolokoltsov, Vassili N. (2022) CTRW modeling of quantum measurement and fractional equations of quantum stochastic filtering and control. Fractional Calculus and Applied Analysis, 25 (1). pp. 128-165. doi:10.1007/s13540-021-00002-2 ISSN 1314-2224.
Kolokoltsov, Vassili N. and Troeva, Marianna (2022) A new approach to fractional kinetic evolutions. Fractal and Fractional, 6 (2). e49. doi:10.3390/fractalfract6020049 ISSN 2504-3110.
Kolokoltsov, V. N. (VasiliÄ Nikitich) (2019) The probabilistic point of view on the generalized fractional PDES. Fractional Calculus and Applied Analysis, 22 (3). pp. 543-600. doi:10.1515/fca-2019-0033 ISSN 1311-0454.
Kolokoltsov, Vassili N. and Troeva, Marianna (2019) On mean field games with common noise and McKean-Vlasov SPDEs. Stochastic Analysis and Applications, 37 (4). pp. 522-549. doi:10.1080/07362994.2019.1592690 ISSN 0736-2994.
Kolokoltsov, V. N. (VasiliÄ Nikitich) and Troeva, M. S. (2018) Regularity and Sensitivity for McKean-Vlasov Type SPDEs Generated by Stable-like Processes. Issues of Analysis, 25 (2). pp. 69-81. doi:10.15393/j3.art.2018.5250 ISSN 2306-3432.
Kolokoltsov, V. N. (VasiliÄ Nikitich) and Malafeyev, O. A. (2018) Corruption and botnet defense : a mean field game approach. International Journal of Game Theory, 47 . pp. 977-999. doi:10.1007/s00182-018-0614-1 ISSN 0020-7276.
Hernández-Hernández, Ma Elena and Kolokoltsov, V. N. (VasiliÄ Nikitich) (2018) Probabilistic solutions to nonlinear fractional differential equations of generalized Caputo and Riemann–Liouville type. Stochastics An International Journal of Probability and Stochastic Processes, 90 (2). pp. 224-255. doi:10.1080/17442508.2017.1334059 ISSN 1744-2508.
Hernández-Hernández, Ma Elena, Kolokoltsov, V. N. (VasiliÄ Nikitich) and Toniazzi, L. (2017) Generalised fractional evolution equations of Caputo type. Chaos, Solitons & Fractals, 102 . pp. 184-196. ISSN 0960-0779.
Kolokoltsov, V. N. (VasiliÄ Nikitich) (2017) The evolutionary game of pressure (or interference), resistance and collaboration. Mathematics of Operations Research, 42 (4). pp. 915-944. doi:10.1287/moor.2016.0838 ISSN 0364-765X.
Hernández-Hernández, Ma Elena and Kolokoltsov, V. N. (VasiliÄ Nikitich) (2016) On the solution of two-sided fractional ordinary differential equations of Caputo type. Fractional Calculus and Applied Analysis, 19 (6). pp. 1393-1413. doi:10.1515/fca-2016-0072 ISSN 1311-0454.
Kolokoltsov, V. N. (VasiliÄ Nikitich) and Bensoussan, A. (2016) Mean-field-game model for botnet defense in cyber-security. Applied Mathematics & Optimization, 74 (3). pp. 669-692. doi:10.1007/s00245-016-9389-6 ISSN 0095-4616.
Hernández-Hernández, Ma Elena and Kolokoltsov, V. N. (VasiliÄ Nikitich) (2016) On the probabilistic approach to the solution of generalized fractional differential equations of Caputo and Riemann-Liouville type. Journal of Fractional Calculus and Applications, 7 (1). pp. 147-175. 14. ISSN 2090-584X.
Kolokoltsov, V. N. (VasiliÄ Nikitich) and Malafeyev, O. A. (2015) Mean-field-game model of corruption. Dynamic Games and Applications . doi:10.1007/s13235-015-0175-x ISSN 2153-0785.
Gorban, A. N., Kolokoltsov, V. N. (VasiliÄ Nikitich) and Yablonsky, G. S. (2015) Generalized mass action law and thermodynamics of nonlinear Markov processes. Mathematical Modelling of Natural Phenomena, 10 (5). pp. 16-46. doi:10.1051/mmnp/201510503 ISSN 0973-5348.
Kolokoltsov, V. N. (VasiliÄ Nikitich) (2015) On fully mixed and multidimensional extensions of the Caputo and Riemann-Liouville derivatives, related Markov processes and fractional differential equations. Fractional Calculus and Applied Analysis, 18 (4). pp. 1039-1073. doi:10.1515/fca-2015-0060 ISSN 1311-0454.
Kolokoltsov, V. N. (VasiliÄ Nikitich) (2015) Stochastic monotonicity and duality of kth order with application to put-call symmetry of powered options. Journal of Applied Probability, 52 (1). pp. 82-101. doi:10.1239/jap/1429282608 ISSN 0021-9002.
Kolokoltsov, V. N. (VasiliÄ Nikitich) and Veretennikova, Maria A. (2014) A fractional Hamilton Jacobi Bellman equation for scaled limits of controlled Continuous Time Random Walks. Communications in Applied and Industrial Mathematics, 6 (1). doi:10.1685/journal.caim.484 ISSN 2038-0909.
Kolokoltsov, V. N. (VasiliÄ Nikitich), Troeva, Marianna and Yang, Wei (2014) On the rate of convergence for the mean-field approximation of controlled diffusions with large number of players. Dynamic Games and Applications, Volume 4 (Number 2). pp. 208-230. doi:10.1007/s13235-013-0095-6 ISSN 2153-0785.
Kolokoltsov, V. N. (VasiliÄ Nikitich) and Veretennikova, M. A. (2014) Well-posedness and regularity of the Cauchy problem for nonlinear fractional in time and space equations. Fractional Differential Calculus, 4 (1). pp. 1-30. doi:10.7153/fdc-04-01 ISSN 1847-9677.
Basna, R., Hilbert, A. and Kolokoltsov, V. N. (VasiliÄ Nikitich) (2014) An epsilon-Nash equilibrium for non-linear Markov games of mean-field-type on finite spaces. Communications on Stochastic Analysis, 8 (4). pp. 449-468. ISSN 0973-9599.
Binner, Jane, Fletcher, Leslie, Kolokoltsov, V. N. (VasiliÄ Nikitich) and Ciardiello, Francesco (2013) External pressure on alliances : what does the prisoners' dilemma reveal? Games , Volume 4 (Number 4). pp. 754-775. doi:10.3390/g4040754 ISSN 2073-4336.
Kolokoltsov, V. N. (VasiliÄ Nikitich) and Lee, Rui Xin (2013) Stochastic duality of Markov processes : a study via generators. Stochastic Analysis and Applications, Volume 31 (Number 6). pp. 992-1023. doi:10.1080/07362994.2013.827098 ISSN 1532-9356.
Kolokoltsov, V. N. (VasiliÄ Nikitich) (2013) Game theoretic analysis of incomplete markets : emergence of probabilities, nonlinear and fractional Black–Scholes equations. Risk and Decision Analysis, Volume 4 (Number 3). pp. 131-161. doi:10.3233/RDA-2011-0062 ISSN 1569-7371.
Kolokolʹtsov, V. N. (Vasiliĭ Nikitich) and Yang, Wei (2013) Existence of solutions to path-dependent kinetic equations and related forward-backward systems. Open Journal of Optimization, Volume 2 (Number 2). pp. 39-44. doi:10.4236/ojop.2013.22006 ISSN 2325-7105.
Kolokoltsov, V. N. (VasiliÄ Nikitich) (2013) Nonlinear diffusions and stable-like processes with coefficients depending on the median or VaR. Applied Mathematics & Optimization, Volume 68 (Number 1). pp. 85-98. doi:10.1007/s00245-013-9199-z ISSN 0095-4616.
Albeverio, Sergio, Hilbert, Astrid and Kolokoltsov, V. N. (VasiliÄ Nikitich) (2012) Uniform asymptotic bounds for the heat kernel and the trace of a stochastic geodesic flow. Stochastics An International Journal of Probability and Stochastic Processes, Volume 84 (Number 2-3). pp. 315-333. doi:10.1080/17442508.2010.519029 ISSN 1744-2508.
Kolokoltsov, V. N. (VasiliÄ Nikitich) (2012) Nonlinear Markov games on a finite state space (mean-field and binary interactions). International Journal of Statistics and Probability, Volume 1 (Number 1). doi:10.5539/ijsp.v1n1p77 ISSN 1927-7032.
Kolokoltsov, V. N. (VasiliÄ Nikitich) and Yang, Wei (2012) Turnpike theorems for Markov games. Dynamic Games and Applications, Volume 2 (Number 3). pp. 294-312. doi:10.1007/s13235-012-0047-6 ISSN 2153-0785.
Kolokoltsov, V. N. (VasiliÄ Nikitich) (2011) Stochastic monotonicity and duality for one-dimensional Markov processes. Mathematical Notes, Vol.89 (No.5-6). pp. 652-660. doi:10.1134/S0001434611050063 ISSN 0001-4346.
Kolokoltsov, V. N. (VasiliÄ Nikitich) (2011) The Lévy–Khintchine type operators with variable Lipschitz continuous coefficients generate linear or nonlinear Markov processes and semigroups. Probability Theory and Related Fields, Vol.151 (No.1-2). pp. 95-123. doi:10.1007/s00440-010-0293-8 ISSN 0178-8051.
Kolokoltsov, V. N. (VasiliÄ Nikitich) (2010) Stochastic integrals and SDE driven by nonlinear Lévy noise. Stochastic Analyisis, Volume 2010 . pp. 227-242. doi:10.1007/978-3-642-15358-7_11
Kolokoltsov, V. N. (VasiliÄ Nikitich) (2010) The central limit theorem for the Smoluchovski coagulation model. Probability Theory and Related Fields, Vol.146 (No.1-2). pp. 87-153. doi:10.1007/s00440-008-0186-2 ISSN 0178-8051.
Kolokoltsov, V. N. (VasiliÄ Nikitich) (2009) Generalized continuous-time random walks, subordination by hitting times, and fractional dynamics. Theory of Probability and its Applications, Vol.53 (No.4). pp. 594-609. doi:10.1137/S0040585X97983857 ISSN 0040-585X.
Kolokoltsov, V. N. (VasiliÄ Nikitich) (2007) Nonlinear Markov semigroups and interacting Lévy type processes. Journal of Statistical Physics, Vol.126 (No.3). pp. 585-642. doi:10.1007/s10955-006-9211-y ISSN 0022-4715.
Hucki, Z. and Kolokoltsov, V. N. (VasiliÄ Nikitich) (2007) Pricing of rainbow options : game theoretic approach. International Game Theory Review, Vol.9 (No.2). p. 215. doi:10.1142/S0219198907001370 ISSN 0219-1989.
Kolokoltsov, V. N. (VasiliÄ Nikitich) and Tyukov, Alexei E. (2006) Boundary-value problems for Hamiltonian systems and absolute minimizers in calculus of variations. Electronic Journal of Differential Equations, Vol.2006 (No.90). pp. 1-21. ISSN 1072-6691.
Kolokoltsov, V. N. (VasiliÄ Nikitich) (2006) Kinetic equations for the pure jump models of k-nary interacting particle systems. Markov Processes and Related Fields, Vol.12 (No.1). pp. 95-138. ISSN 1024-2953.
Kolokoltsov, V. N. (VasiliÄ Nikitich) (2006) On the regularity of solutions to the spatially homogeneous Boltzmann equation with polynomially growing collision kernel. Advanced Studies in Contemporary Mathematics, Vol.12 (No.1). ISSN 1229-3067.
Kolokoltsov, V. N. (VasiliÄ Nikitich), Schilling, René L. and Tyukov, Alexei E. (2004) Estimates for multiple stochastic integrals and stochastic Hamilton-Jacobi equations. Revista Matematika Iberoamerikana, Vol.20 (No.2). pp. 333-380.
Kolokoltsov, V. N. (VasiliÄ Nikitich) (2004) Hydrodynamic limit of coagulation-fragmentation type models of k-nary interacting particles. Journal of Statistical Physics, Vol.115 (No.5/6). pp. 1621-1653. doi:10.1023/B:JOSS.0000028071.96950.12 ISSN 0022-4715.
Kolokoltsov, V. N. (VasiliÄ Nikitich) (2004) Measure-valued limits of interacting particle systems with k-nary interactions. II, Finite-dimensional limits. Stochastics and Stochastics Reports, Vol.76 (No.1). pp. 45-58. doi:10.1080/10451120410001661241 ISSN 1045-1129.
Kolokoltsov, V. N. (VasiliÄ Nikitich) (2004) On Markov processes with decomposable pseudo-differential generators. Stochastics and Stochastics Reports, Vol.76 (No.1). pp. 1-44. doi:10.1080/10451120410001661250 ISSN 1045-1129.
Belavkin, V. P. and Kolokoltsov, V. N. (VasiliÄ Nikitich) (2003) On a general kinetic equation for many-particle systems with interaction, fragmentation and coagulation. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol.459 (No.2031). pp. 727-748. doi:10.1098/rspa.2002.1026 ISSN 1364-5021.
Kolokoltsov, V. N. (VasiliÄ Nikitich) (2003) On extensions of mollified Boltzmann and Smoluchowski equations to particle systems with a k-ary interaction. Russian Journal of Mathematical Physics, Vol.10 (No.3). pp. 268-295. ISSN 1555-6638 .
Belavkin, V. P. and Kolokoltsov, V. N. (VasiliÄ Nikitich) (2002) Stochastic evolution as a quasiclassical limit of a boundary value problem for Schrödinger equations. Infinite Dimensional Analysis, Quantum Probability and Related Topics, Vol.5 (No.1). pp. 61-91. doi:10.1142/S0219025702000717 ISSN 0219 0257.
Kolokoltsov, V. N. (VasiliÄ Nikitich), Schilling, René L. and Tyukov, Alexei E. (2002) Transience and non-explosion of certain stochastic Newtonian systems. Electronic Journal of Probability, Vol.7 (No.19). ISSN 1083-6489.
Kolokoltsov, V. N. (VasiliÄ Nikitich) (2001) Idempotent structures in optimization. Journal of Mathematical Sciences, Vol.104 (No.1). pp. 847-880. doi:10.1023/A:1009514904187 ISSN 10723374.
Kolokoltsov, V. N. (VasiliÄ Nikitich) (2001) Small diffusion and fast dying out asymptotics for superprocesses as non-Hamiltonian quasiclassics for evolution equations. Electronic Journal of Probability, Vol.6 (No.21). ISSN 1083-6489.
Kolokoltsov, V. N. (VasiliÄ Nikitich) (1998) Nonexpansive maps and option pricing. Kibernetika, Vol.34 (No.6). pp. 713-724. ISSN 1019-5262.
Book Item
Cecchin, A and Kolokoltsov, V. N. (2018) Evolutionary game of coalition building under external pressure. In: Apaloo, J. and Viscolani, B., (eds.) Advances in Dynamic and Mean Field Games. ISDG 2016. Annals of the International Society of Dynamic Games. Annals of the International Society of Dynamic Games, 15 . Cham: Birkhaeuser Verlag AG, pp. 71-106. ISBN 9783319706184
Binner, Jane M., Fletcher, Leslie and Kolokoltsov, V. N. (VasiliÄ Nikitich) (2013) Existence and uniqueness of Nash equilibria in a simple Lanchester model of the costs of customer churn. In: Petrosjan, L. and Mazalov, V., (eds.) Game Theory and Applications. Nova Science Publishers, pp. 19-26. ISBN 9781626184534
Kolokoltsov, V. N. (VasiliÄ Nikitich) (2012) Nonlinear Levy and nonlinear Feller processes : an analytic introduction. In: Antoniouk, A. V. and Melnik, R. V., (eds.) Mathematics and Life Sciences. De Gruyter, pp. 45-68. ISBN 9783110288537
Kolokoltsov, V. N. (VasiliÄ Nikitich) (2005) Path integration : connecting pure jump and Wiener processes. In: Waymire, Edward C. and Duan, Jinqiao, (eds.) Probability and partial differential equations in modern applied mathematics. IMA volumes in mathematics and its applications, Vol.140 . Springer Basel AG: Birkhäuser, pp. 163-180. ISBN 0387258795
Akian, Marianne, Gaubert, S. (Stephane) and Kolokoltsov, V. N. (VasiliÄ Nikitich) (2005) Set coverings and invertibility of functional Galois connections. In: Litvinov, G. L. (GrigoriÄ Lazarevich), 1944- and Maslov, V. P. (Viktor Pavlovich), (eds.) Idempotent Mathematics and Mathematical Physics. Washington DC, USA: American Mathematical Society , pp. 19-51. ISBN 0-8218-3538-6
Grosskinsky, Stefan Interacting particle systems. In: Kolokoltsov, V. N. (VasiliÄ Nikitich) and MacKay, R. S., (eds.) Lecture Notes in Complexity Science. UNSPECIFIED.
Book
Kolokoltsov, V. N. (VasiliÄ Nikitich) (2010) Nonlinear Markov processes and kinetic equations. Cambridge tracts in mathematics (No.182). Cambridge ; New York: Cambridge University Press. ISBN 9780521111843
Kolokoltsov, V. N. (VasiliÄ Nikitich) and Malafeyev, Oleg A. (2010) Understanding game theory : introduction to the analysis of many agent systems with competition and cooperation. Singapore ; London: World Scientific. ISBN 9789814291712
This list was generated on Thu Mar 28 10:13:25 2024 GMT.