Handbook of Stochastic Analysis and Applications (Statistics: A Series of Textbooks and Monographs)

Twelve contributions from mathematicians in the U.S., Russia, China, and Israel present an overview of the analysis of some basic stochastic processes and stochastic equations as well as certain of their applications. Chapters in the first half of the text are devoted largely to theory, while the remainder focus on applications. A sampling of topics includes Markov processes, semimartingales, Hida's white noise theory, large deviations, control theory, stochastic game theory, and the application of optimization problems to financial mathematics. An introduction to general theories of stochastic processes and modern martingale theory. The volume focuses on consistency, stability and contractivity under geometric invariance in numerical analysis, and discusses problems related to implementation, simulation, variable step size algorithms, and random number generation. For the most part in this chapter we will confine ourselves to time-homogeneous Markov processes.