Existence of Solutions to Path-Dependent Kinetic Equations and Related Forward-Backward Systems

Vassili Kolokoltsov, Wei Yang

Department of Mathematics and Statistics, University of Strathclyde, Glasgow, UK.
Department of Statistics, University of Warwick, Coventry, UK.

DOI: 10.4236/ojop.2013.22006                

Abstract

This paper is devoted to path-dependent kinetics equations arising, in particular, from the analysis of the coupled backward-forward systems of equations of mean field games. We present local well-posedness, global existence and some regularity results for these equations.

Keywords

Kinetic Equation; Mean Field Control; Global Existence; Path Dependence; Nonlinear Markov Process; Coupled Backward-Forward Systems

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	V. N. Kolokoltsov, “Nonlinear Markov Processes and Kinetic Equations. Cambridge Tracks in Mathematics 182,” Cambridge University Press, Cambridge, 2010.
[2]	O. Guéant, J.-M. Lasry and P.-L. Lions, “Mean Field Games and Applications. Paris-Princeton Lectures on Mathematical Finance 2010,” Springer, Berlin, pp. 205-266.
[3]	M. Huang, R. P. Malhamé and P. E. Caines, “Large Population Stochastic Dynamic Games: Closed-Loop MckeanVlasov Systems and the Nash Certainty Equivalence Principle,” Communications in Information and Systems, Vol. 6, No. 3, 2006, pp. 221-252.
[4]	V. N. Kolokoltsov, J. J. Li and W. Yang, “Mean Field Games and Nonlinear Markov Processes,” 2011. arXiv:1112.3744v2
[5]	V. N. Kolokoltsov, “Markov Processes, Semigroups and Generators,” De Gryuter, 2011.
[6]	V. N. Kolokoltsov, “Nonlinear Diffusions and StableLike Processes with Coefficients Depending on the Median or VaR,” Applied Mathematics and Optimization, 2012. http://arxiv.org/abs/1207.5925
[7]	D. Crisan, Th. Kurtz and Y. Lee, “Conditional Distributions, Exchangeable Particle Systems, and Stochastic Partial Differential Equations,” Preprint, 2012.