Introduction to probability and stochastic processes with applications. (Q2889250)

The book is designed for an introductory course at a university on probability, processes and stochastic modelling. It is a reader friendly book. Basic concepts, probability distributions, limit theorems and stochastic processes are given not only in the explanatory text, but also in various examples and exercises (the later with solutions). The examples and exercises give a very good instructive and suggestive possibility for an orientation in the concepts and matters of probability. This holds also for the explanation of all other terms in the book. The detailed structure of the text is evident from the fact that, e.g., a special chapter (29 pages out of 589) is devoted to the theory of conditional expectations. An introduction to martingales and to the Brownian motion is presented. Stochastic calculus (especially Itō calculus) is presented via the stochastic integral of a process \(X_t\;(t \leq 0)\) with respect to the Brownian motion. Also, discrete- and continuous-time models of markets are studied.