2019

Kolokoltsov, V. N. (Vasiliĭ 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

Kolokoltsov, Vassili N. and Troeva, Marianna (2019) On mean field games with common noise and McKean-Vlasov SPDEs. Stochastic Analysis and Applications . doi:10.1080/07362994.2019.1592690 (In Press)

2018

Kolokoltsov, V. N. (Vasiliĭ 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

Kolokoltsov, V. N. (Vasiliĭ Nikitich) and Malafeyev, O. A. (2018) Corruption and botnet defense : a mean field game approach. International Journal of Game Theory . doi:10.1007/s00182-018-0614-1 (In Press)

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

Hernández-Hernández, Ma Elena and Kolokoltsov, V. N. (Vasiliĭ 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

2017

Hernández-Hernández, Ma Elena, Kolokoltsov, V. N. (Vasiliĭ Nikitich) and Toniazzi, L. (2017) Generalised fractional evolution equations of Caputo type. Chaos, Solitons & Fractals, 102 . pp. 184-196.

Kolokoltsov, V. N. (Vasiliĭ 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

2016

Hernández-Hernández, Ma Elena and Kolokoltsov, V. N. (Vasiliĭ 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

Kolokoltsov, V. N. (Vasiliĭ 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

Hernández-Hernández, Ma Elena and Kolokoltsov, V. N. (Vasiliĭ 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.

2015

Kolokoltsov, V. N. (Vasiliĭ Nikitich) and Malafeyev, O. A. (2015) Mean-field-game model of corruption. Dynamic Games and Applications . doi:10.1007/s13235-015-0175-x

Gorban, A. N., Kolokoltsov, V. N. (Vasiliĭ 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

Kolokoltsov, V. N. (Vasiliĭ 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

Kolokoltsov, V. N. (Vasiliĭ 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

2014

Kolokoltsov, V. N. (Vasiliĭ 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

Kolokoltsov, V. N. (Vasiliĭ 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

Kolokoltsov, V. N. (Vasiliĭ 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

Basna, R., Hilbert, A. and Kolokoltsov, V. N. (Vasiliĭ 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.

2013

Binner, Jane, Fletcher, Leslie, Kolokoltsov, V. N. (Vasiliĭ 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

Kolokoltsov, V. N. (Vasiliĭ 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

Kolokoltsov, V. N. (Vasiliĭ 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

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

Binner, Jane M., Fletcher, Leslie and Kolokoltsov, V. N. (Vasiliĭ 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. (Vasiliĭ 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

2012

Kolokoltsov, V. N. (Vasiliĭ 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

Albeverio, Sergio, Hilbert, Astrid and Kolokoltsov, V. N. (Vasiliĭ 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

Kolokoltsov, V. N. (Vasiliĭ 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

Kolokoltsov, V. N. (Vasiliĭ 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

2011

Kolokoltsov, V. N. (Vasiliĭ 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

Kolokoltsov, V. N. (Vasiliĭ 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

2010

Kolokoltsov, V. N. (Vasiliĭ 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. (Vasiliĭ 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

Kolokoltsov, V. N. (Vasiliĭ 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. (Vasiliĭ 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

2009

Kolokoltsov, V. N. (Vasiliĭ 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

2007

Kolokoltsov, V. N. (Vasiliĭ 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

Hucki, Z. and Kolokoltsov, V. N. (Vasiliĭ Nikitich) (2007) Pricing of rainbow options : game theoretic approach. International Game Theory Review, Vol.9 (No.2). p. 215. doi:10.1142/S0219198907001370

2006

Kolokoltsov, V. N. (Vasiliĭ 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.

Kolokoltsov, V. N. (Vasiliĭ 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.

Kolokoltsov, V. N. (Vasiliĭ 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).

2005

Kolokoltsov, V. N. (Vasiliĭ 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. (Vasiliĭ Nikitich) (2005) Set coverings and invertibility of functional Galois connections. In: Litvinov, G. L. (Grigoriĭ 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

2004

Kolokoltsov, V. N. (Vasiliĭ 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. (Vasiliĭ 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

Kolokoltsov, V. N. (Vasiliĭ 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

Kolokoltsov, V. N. (Vasiliĭ 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

2003

Belavkin, V. P. and Kolokoltsov, V. N. (Vasiliĭ 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

Kolokoltsov, V. N. (Vasiliĭ 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.

2002

Belavkin, V. P. and Kolokoltsov, V. N. (Vasiliĭ 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

Kolokoltsov, V. N. (Vasiliĭ 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).

2001

Kolokoltsov, V. N. (Vasiliĭ Nikitich) (2001) Idempotent structures in optimization. Journal of Mathematical Sciences, Vol.104 (No.1). pp. 847-880. doi:10.1023/A:1009514904187

Kolokoltsov, V. N. (Vasiliĭ 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).

1998

Kolokoltsov, V. N. (Vasiliĭ Nikitich) (1998) Nonexpansive maps and option pricing. Kibernetika, Vol.34 (No.6). pp. 713-724.