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An optimal control problem is considered for a stochastic differential equation containing a statedependent regime switching, with a recursive cost functional. Due to the non-exponential discounting in the cost functional, the problem is time-inconsistent in general. Therefore, instead of finding a global optimal control (which is not possible), we look for a time-consistent (approximately) locally optimal equilibrium strategy. Such a strategy can be represented through the solution to a system of partial differential equations, called an equilibrium Hamilton-Jacob-Bellman (HJB, for short) equation which is constructed via a sequence of multi-person differential games. A verification theorem is proved and, under proper conditions, the well-posedness of the equilibrium HJB equation is established as well.

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Please cite this article as: H. Mei, G. Yin, Convergence and convergence rates for approximating ergodic means of functions of solutions to stochastic differential equations with Markov switching, Stochastic Processes and their Applications (2015), http://dx. AbstractThis work focuses on numerical algorithms for approximating the ergodic means for suitable functions of solutions to stochastic differential equations with Markov regime switching. Our main effort is devoted to obtaining the convergence and rates of convergence of the approximation algorithms. The study is carried out by obtaining laws of large numbers and laws of iterated logarithms for numerical approximation to long-run averages of suitable functions of solutions to switching diffusions.

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