Share This Article:

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

Abstract Full-Text HTML Download Download as PDF (Size:163KB) PP. 39-44
DOI: 10.4236/ojop.2013.22006    2,377 Downloads   4,873 Views   Citations

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.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

V. Kolokoltsov and W. Yang, "Existence of Solutions to Path-Dependent Kinetic Equations and Related Forward-Backward Systems," Open Journal of Optimization, Vol. 2 No. 2, 2013, pp. 39-44. doi: 10.4236/ojop.2013.22006.

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.

  
comments powered by Disqus

Copyright © 2019 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.