Mean field games are studied in the framework of controlled martingale problems, and general existence theorems are proven in which the equilibrium control is Markovian. The framework is flexible enough to include degenerate volatility, which may depend on both the control and the mean field....

We consider the Skorokhod problem in a time-varying interval. We prove existence and uniqueness of the solution. We also express the solution in terms of an explicit formula. Moving boundaries may generate singularities when they touch. Under the assumption that the first time [tau] when the...

We analyse the quasi-stationary distributions of the family of Markov chains {Xn[var epsilon]},[var epsilon]0, obtained from small non-local random perturbations of iterates of a map f : I--I on a compact interval. The class of maps considered is slightly more general than the class of...

We consider the exponential decay rate of the stationary tail probabilities of reflected Brownian motion X in the N-dimensional orthant having drift b, covariance matrix A, and constraint matrix D. Suppose that the Skorokhod or reflection mapping associated with the matrix D is well-defined and...