ABSTRACT
This introduction presents an overview of the key concepts discussed in the subsequent chapters of this book. The book presents axiomatic probability theory that has considerable intuitive content, particularly in the context of decision making under uncertainty. It describes the families of sigma-fields represent information flow; stopping times are closely associated with decision strategies; martingale properties characterize optimal decisions; and so on. There is far more to it than an arid concern for mathematical rectitude The book summarizes those notions and results in probability and stochastic process theory. Some effort has been made to keep these prerequisites to a minimum, and only the basic facts about probability spaces, integration, continuous-time stochastic processes and Markov processes are needed. The book explains cover probability and stochastic processes and deals with Markov processes, with the emphasis on the so-called differential generator of a Markov process which plays such a major role.
