Markov processes and their applications (Q2784989)

The article under review, the first chapter of the volume ``The Handbook of Stochastic Analysis and Their Applications'', is a detailed survey consisting of the following sections: 1. Introduction, 2. Markov chains, 3. Discrete parameter Markov processes on general state spaces, 4. Continuous time Markov processes, 5. Markov processes and semigroup theory, 6. Stochastic differential equations. NEWLINENEWLINENEWLINEThe author has pains to present the subject lucidly without sacrifice of rigour. While presenting the semigroup structure of Markov processes, the author has chosen a right blend of analysis and probability elements. In the final chapter on stochastic differential equations, the original motivation of Itô in the formulation of the stochastic integral is brought out in the right perspective; in fact all the aspects of modern stochastic calculus are presented in a crisp manner. The article is commended for new entrants to the subject.NEWLINENEWLINEFor the entire collection see [Zbl 0979.00017].