# Professor Vassili Kolokoltsov (Emeritus Professor)

General research interests: probability and stochastic processes, optimization and games with applications to business, biology and finances, mathematical physics, differential equations and functional analysis.

Applications from perspective PhD students are welcome.

Publications: more than 100 papers and several monographs, see selected earlier reprints below and the list of main publications in CV, (on the right side of this page).

The drafts of most of the recent publications can be found on ArXiv:

http://arxiv.org/find/grp_math/1/au:+kolokoltsov/0/1/0/all/0/1

Teaching 2006-2019: 'Probability A and B' for the first year students, see ProbBlectnotes; 'Advanced probability' for the third year, 'Brownian motion', see BMlectnotes, and 'Stochastic methods in Finances', see FinanceExercises for final years MMORSE, 2020: Life Contingencies.

I am planning to run the 4 months program on Fractional Differential equations in the Newton Institute, Cambridge, in Jan-Apr 2021 (now rescheduled to Jan-Apr 2022!)

My **talks **in 2009-2011: Talks My **books****: **monographs

I received** ** the** St. Petersburg University award** 'Research work in 2011' for the book 'Understanding Game Theory' (jointly with O. A. Malafeyev)

Current Member of the Editorial Boards of the international journals:

The 'Dynamic Games and Applications' (2013 -)

The Open Journal of Optimization OJO, (2012 -)

Fractional Differential Calculus (FDC), see http://ele-math.com/ (2014 -)

Asia Pacific Journal of Mathematics (2014 - ), see http://apjm.apacific.org/

Issues of Analysis (2013 - ), see http://issuesofanalysis.petrsu.ru/

Fractal and Fractional, MDPI (2019- ), https://www.mdpi.com/journal/fractalfract/editors

Fractional Calculus and Applied Analysis FCAA (2019- )

**PhD students**:11 completed successfully, current:

Li Zeng (2nd year, Game theory) and Howard Su (1st year, Financial Maths and Machine Learning)

**Conference organization 2010-2014**:

The fifth Warwick School-Conference on Control and Games, Warwick 29th Apr - 2 May 2014

The fourth Warwick School-Conference on Control and Games, Warwick 7-10 May 2013

'From Mean-Field Control to Weak KAM theory' , Warwick 7 - 10 May 2012

http://www2.warwick.ac.uk/fac/sci/maths/research/events/2009_2010/symposium/gamwks/ , 2010,

Slides and pictures: http://www2.warwick.ac.uk/fac/sci/statistics/staff/academic/kolokoltsov/gam10slides/

'SIAM conference on Control and its Applications', July 2011: http://www.siam.org/meetings/ct11/

Satellite 'Trends in game theory' to ECCS 2011: http://eccs2011.eu/

**Some old papers:**

**V. N. Kolokoltsov** (2011) Nonlinear Levy and nonlinear Feller processes,

http://arxiv.org/abs/1103.5591 Published in De Gruyter ``Mathematics and Life Sciences'' 2013, p. 45-70.

**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;

V. Kolokoltsov. Nonexpansive maps and option pricing. Kibernetika 34:6 (1998), 713-724.

V. Kolokoltsov. Idempotent Structures in Optimization. Journal Math. Sci. New York 104:1 (2001), 847-880.

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.

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.

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;

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.

V.N. Kolokoltsov.* *On Markov processes with decomposable pseudo-differential generators.

* *Stochastics and Stochastics Reports 76:1 (2004), 1-44.

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*.*

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;

V. Kolokoltsov. Hydrodynamic limit of coagulation-fragmentation type models of k -nary interacting particles.

* *Journ. Stat. Physics 115, 5/6 (2004), 1621-1653;

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;

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.

V.N. Kolokoltsov. Small diffusion and fast dying out asymptotics for superprocesses as non-Hamiltonian quasi-classics for evolution equations.

Electronic J. of Probability 6 (2001), paper 21.