Dr Vassili Kolokoltsov
Reader in Probability from June 2006, promoted to professor from 1st June 2012
General research interests: probability and stochastic processes, mathematical physics, differential equations and functional analysis, optimization and games with applications to business, biology and finances. Applications from perspective PhD students are welcome.
Publications: more than 100 papers and several monographs (see selected reprints below and the list of main publications in CV ).
Teaching 2006-: 'Probability A and B' for the first year students, see ProbBlectnotes; 'Brownian motion', see BMlectnotes, and 'Stochastic methods in Finances', see FinanceExercises and Tests 2010-2011, for final years MMORSE.
Departmental administration duty: Chair of the Research Committee, Organization of the final year research projets, Links with Complexity Center
Slides of my recent talks: Recent talks
My books: monographs
Some recent highlights:
St. Petersburg University award 'Research work in 2011' for the book 'Understanding Game Theory' (jointly with O. A. Malafeyev)
I am organising workshop 'From Mean-Field Control to Weak KAM theory' (registration free)
$420,000 US grant for three year research in 'Nonlinear Markov games'
Current PhD students:
T. Lapinski (Quantum Economics)
R. Lee (Stochastic monotonicity, duality and applications)
Jiajie Li (Mean field games)
M. Veretennikova (Controlled fractional dynamics)
Lu Zou (Order book modelling in finances)
I have organised a workshop on game theory, see
http://www2.warwick.ac.uk/fac/sci/maths/research/events/2009_2010/symposium/gamwks/
Slides of the talks and pictures: http://www2.warwick.ac.uk/fac/sci/statistics/staff/academic/kolokoltsov/gam10slides/
I took part in the organization of the 'SIAM conference on Control and its Applications', July 2011, Baltimore (Maryland US)
see: http://www.siam.org/meetings/ct11/
I co-organised (together with M. Kirkilionis and J. Hofbauer) a satellite workshop 'Trends in game theory' to Complexity Science Conference, Sept. 2011, Vienna
see: http://eccs2011.eu/
I have joined the Advisory Panel for the Journal of Physics A (2011)
Some of my preprints are available below:
More recent:
V. Kolokoltsov. Nonlinear Markov games on a finite state space (mean-field and binary interactions)
http://arxiv.org/abs/1105.3053.
International Journal of Statistics and Probability.
Canadian Center of Science and Education (Open access journal), 1:1 (2012), 77-91.
http://www.ccsenet.org/journal/index.php/ijsp/article/view/16682
V. Kolokoltsov and Wei Yang. The turnike theorems for Markov games (2012).
http://arxiv.org/abs/1203.6553. To appear in ``Dynamic Games and Applications''.
V. Kolokotsov and M. Veretennikova. Controlled CTRW and Fractional HJB equations (2012).
http://arxiv.org/abs/1203.6333
V. N. Kolokoltsov and O. A. Malafeyev. On some models of many agent systems with competition and cooperation (2012). http://arxiv.org/abs/1201.1745
Vassili N.Kolokoltsov, Jiajie Li and Wei Yang (2011). Mean Field Games and Nonlinear Markov Processes.
arXiv:1112.3744
V. N. Kolokoltsov (2011) Game theoretic analysis of incomplete markets: emergence of probabilities,
nonlinear and fractional Black-Scholes equations.
http://arxiv.org/abs/1105.3053. To appear in ``Risk and Decision Analysis''.
V. N. Kolokoltsov (2011) Nonlinear Levy and nonlinear Feller processes,
http://arxiv.org/abs/1103.5591 To appear in De Gruyter volume ``Mathematics and Life Sciences''.
V. N. Kolokoltsov (2010) Stochastic monotonicity and duality for one-dimensional Markov processes.
arXiv:1002.4773. Mathematical Notes 89:5 (2011), 652-660.
V. Kolokoltsov (2008). The Levy-Khintchine type operators with variable Lipschitz continuous coefficients generate linear or nonlinear Markov processes and semigroups
arxive http://arxiv.org/abs/0911.5688v1 Prob. Theory Related Fields 151 (2011), 95-123.
V. Kolokoltsov (2007). The Central Limit Theorem for the Smoluchowski Coagulation Model
arXiv:0708.0329v1 [math.PR]. Probability Theory Related Fields 146: 1 (2010), 87-153.
V. Kolokoltsov (2007). Generalized Continuous-Time Random Walks (CTRW), Subordination by Hitting Times and Fractional Dynamics
arXiv:0706.1928v1[math.PR]. Theory of Probability and its Applications 53:4 (2009), 594-609.
V. Kolokoltsov. Nonlinear Markov Semigroups and Interacting Levy Type Processes.
Journ. Stat. Physics 126:3 (2007), 585-642.
V. Kolokoltsov. Kinetic equations for the pure jump models of k -nary interacting particle systems.
Markov Processes and Related Fields 12 (2006), 95-138.
Z. Hucki, V. Kolokoltsov. Pricing of rainbow options: game theoretic approach.
International Game Theory Review 9:2 (2007), 215-242.
V. Kolokoltsov. On the regularity of solutions to the spatially homogeneous Boltzmann equation with polynomially growing collision kernel.
Advanced Stud. Contemp. Math. 12:1 (2006), 9-38.
V.N. Kolokoltsov, A.E. Tyukov. On boundary Value Problems for Hamiltonian Systems and Absolute Minimizers in Calculus of Variations. Electronic J. Dif. Eqns. 2006 (2006), n. 90, 1-21.
V.N. Kolokoltsov. Path integration: connecting pure jump and Wiener processes. In: Waymire, J. Duan (Eds.).
"Probability and Partial Differential Equations in Modern Applied Mathematics" (2005), p. 163-180;
Other:
(1) V. Kolokoltsov. Nonexpansive maps and option pricing. Kibernetika 34:6 (1998), 713-724.
(2) V. Kolokoltsov. Idempotent Structures in Optimization. Journal Math. Sci. New York 104:1 (2001), 847-880.
(3) V.P. Belavkin, V.N. Kolokoltsov. Stochastic evolution as interaction representation of a boundary value problem for Dirac type equation.
Infinite Dimensional Analysis, Quantum Probability and Related Fields 5:1 (2002), 61-92.
(4) V.P. Belavkin, V.N. Kolokoltsov. On general kinetic equation for many particle systems with interaction, fragmentation and coagulation.
Proc. Royal Society London A 459 (2003), issue 2031, 727-748.
(5) V.N. Kolokoltsov, R.L. Schilling, A.E. Tyukov. Estimates for Multiple Stochastic Integrals and stochastic Hamilton-Jacobi equations.
Revista Matematika Iberoamerikana 20 (2004), 333-380;
(6) V. Kolokoltsov. On Extensions of Mollified Boltzmann and Smoluchovski Equations to Particle Systems with a k-ary Interaction.
Russian Journal of Mathematical Physics 10:3 (2003), 268-295.
(7) V.N. Kolokoltsov. On Markov processes with decomposable pseudo-differential generators.
Stochastics and Stochastics Reports 76:1 (2004), 1-44.
(8) V. Kolokoltsov. Measure-valued limits of interacting particle systems with k-ary interaction I . One-dimensional limits.
Probability Theory Related Fields 126 (2003), 364-394.
(9) V. Kolokoltsov. Measure-valued limits of interacting particle systems with k -nary interaction II. Finite-dimensional limits .
Stochastics and Stochastics Reports 76:1 (2004), 45-58;
(10) V. Kolokoltsov. Hydrodynamic limit of coagulation-fragmentation type models of k -nary interacting particles.
Journ. Stat. Physics 115, 5/6 (2004), 1621-1653;
(11) M. Akian, S. Gaubert, V.N. Kolokoltsov. Set Coverings and the Invertibility of Functional Galois Connections.
In: "Idempotent Mathematics in Mathematical Physics" (Eds. G.L. Litvinov and V.P. Maslov), Contemporary Mathematics Series v. 377, AMS (2005), 19-51;
(12) V.N. Kolokoltsov, R.L. Schilling, A.E. Tyukov. Transience and non-explosion of certain stochastic Newtonian systems.
Electronic J. of Probability 7 (2002), Paper 19.
(13) V.N. Kolokoltsov. Smal diffusion and fast dying out asymptotics for superprocesses as non-Hamiltonian quasi-classics for evolution equations.
Electronic J. of Probability 6 (2001), paper 21.
Currently I am editing (together with R. Ball and Robert MacKay) a book of Lecture Notes for Complexity Masters program
