References
- H. Amann, Ordinary Differential Equations, An Introduction to Nonlinear Analysis, de Gruyter Studies in Mathematics Vol. 13, Walter de Gruyter, New york, 1990.
- D. Applebaum, Lévy Processes and Stochastic Calculus, 2nd ed., Cambridge University Press, New York, 2009.
- E. Bandini and M. Fuhrman, Constrained BSDEs representation of the value function in optimal control of pure jump Markov processes, preprint (2015). Available at arXiv:1501.04362.
- R. Basna, A. Hilbert, and V. Kolokoltsov, An epsilon-Nash equilibrium for non-linear Markov games of mean-field-type on finite state space, Commun. Stoch. Anal. 8(4) (2015), pp. 449–468.
- J. Bell, The narrow topology on the set of Borel probability measures on a metrizable space, preprint (2015). Available at http://individual.utoronto.ca/jordanbell/.
- A. Bensoussan and J. Frehse, Control and Nash games with mean-field effect, in Partial Differential Equations: Theory, Control and Approximation, P.G. Ciarlet, T. Li, and Y. Maday, eds., Springer-Verlag, Berlin, 2014, pp. 1–39.
- R. Carmona and F. Delarue, Probabilistic analysis of mean-field games, SIAM J. Control Optim 51(4) (2012), pp. 2705–2734.
- J.A. van Casteren, Markov Processes, Feller Semigroups and Evolutions Equations, Vol. 12, World Scientific, Singapore, 2011.
- M.G. Crandell and T.M. Liggett, Generation of semi-groups of non-linear transformations on general Banach spaces, Am. J. Math. 93(2) (1971), pp. 265–298.
- P. Drabek and J. Milota, Methods of Nonlinear Analysis: Applications to Differential Equations, Springer Science & Business Media, Basel, 2013.
- S. Ethier and Th. Kurtz, Markov Processes: Characterization and Convergence, Wiley Series in Probability and Statistics Vol. 623, John Wiley \ & Sons, New York, 2005.
- W. Fleming and R. Rishel, Deterministic and Stochastic Optimal Control, Springer-Verlag, Berlin, 1975.
- D. Gomes, J. Mohr, and R. Sousa, Continuous time finite state space mean-field games, in Annual Allerton Conference on Communication, Control, and Computing, Allerton, 2013.
- O. Guéant, J.M. Larsy, and P.L. Lions, Mean-field games and applications, in Paris-Princeton Lectures on Mathematical Finance, R. Carmona, E. Çınlar, I. Ekeland, E. Jouini, J.A. Scheinkman, and N. Touzi, eds., Springer-Verlag, Berlin, 2010, pp. 205–266.
- H. Huang, P.E. Caines, and R.P. Malhamé, Large population stochastic dynamic games: Closed-loop McKean--Vlasov systems and the Nash certainty equivalence principle, Commun. Inform. Syst. 6 (2006), pp. 221–252.
- O. Kallenberg, Foundations of Modern Probability, Springer-Verlag, New York, 2002.
- V. Kolokoltsov and W. Yang, Sensitivity analysis for HJB equation with an application to coupled backward-forward system, preprint (2012). Available at arXiv, math. arXiv:1203.5753v2.
- V. Kolokoltsov, Non Linear Markov Processes and Kinetic Equations, Cambridge Tracts in Mathematics, Cambridge University Press, Cambridge, 2010.
- V. Kolokoltsov, Markov Processes, Semi groups, and Generators, de Gruyter Studies in Mathematics, De Gruyter, Berlin, 2011.
- V. Kolokoltsov, Nonlinear Lévy and nonlinear Feller Processes: An analytic introduction, in Mathematics and Life Sciences, A.V. Antoniouk and R.V. Melnik, eds., De Gruyter, Berlin, 2012, pp. 45–68.
- V. Kolokoltsov, The evolutionary game of pressure (or interference), resistance and collaboration, preprint (2014). Available at arXiv, math. arXiv:1412.1269.
- V. Kolokoltsov, M. Troeva, and W. Yang, On the rate of convergence for the mean-field approximation of controlled diffusions with large number, Dyn. Games Appl. 4 (2012), pp. 208–230.
- V. Kolokoltsov and W. Yang, Existence of solutions to path-dependent kinetic equations and related forward-backward systems, Open J. Optim. 6 (2013), pp. 39–44.
- S. Lang, Analysis 1, Addison-Wesley, Manila, 1968.
- J.M. Larsy and P.L. Lions, Mean-field games, Jpn. J. Math. 2 (2007), pp. 229–260.
- A. Lasota and C.M. Mackey, Chaos, Fractals, and Noise: Stochastic Aspects of Dynamics (Applied Mathematical Sciences), Springer, New York, 1998.
- C.R. McOwen, Partial Differential Equations: Methods and Applications, Pearson Education, New York, 2003.
- K. Oelschläger, A martingale approach to the law of aarge numbers for weakly interacting stochastic processes, Ann. Probab. 12(2) (1982), pp. 458–479.
- R. Pliska, Controlled jump processes. Stoch. Process. Appl. (1975), pp. 259–282.
- R. Pliska, A Semigroup representation of the maximum expected reward vector in continuous parameter Markov decision theory, SIAM J. Control. 13(6) (1975), pp. 1115–1129.
- M. Reed and B. Simon, Methods of Modern Mathematical Physics, Functional Analysis, Academic Press, New York, 1980.
- E. Taylor, Measure Theory and Integration, Graduate Studies in Mathematics, American Mathematical Society, Providence, 2006.