This book presents results including asymptotic expansions of probability vectors, structural properties of occupation measures, exponential bounds, aggregation and decomposition and associated limit processes, and interface of discrete-time and continuous-time systems.  One of the salient features is that it contains a diverse range of applications on filtering, estimation, control, optimization, and Markov decision processes, and financial engineering.  This book will be an important reference for researchers in the areas of applied probability, control theory, operations research, as well as for practitioners who use optimization techniques.  Part of the book can also be used in a graduate course of applied probability, stochastic processes, and applications.