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.