×

Lectures on stochastic processes. Notes by K. Muralidhara Rao. Reissued ed. (English) Zbl 0561.60068

This excellent introductory course to the modern theory of Markov processes discusses the general properties of generators of the semigroups of linear operators defined by the transition probabilities. Strong Markov processes and their generators in the restricted sense are also considered. General theory is illustrated by considering the multi- dimensional Brownian motion and additive processes.
The main results of the classical potential theory are deduced using properties of the Brownian motion. A stochastic calculus with respect to the Brownian motion is developed and diffusion processes are constructed as solutions of stochastic differential equations. The course is finished by Feller’s theory of one-dimensional diffusions.
Reviewer: B.Grigelionis

MSC:

60Jxx Markov processes
60-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to probability theory
60J25 Continuous-time Markov processes on general state spaces
60J60 Diffusion processes
60H05 Stochastic integrals
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)