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Markov processes. (Russian) Zbl 0727.60071
Itogi Nauki Tekh., Ser. Sovrem. Probl. Mat., Fundam. Napravleniya 46, 248 p. (1989).
This is an expound of the contemporary state of the theory of Markov processes. Contents is divided into five chapters: 1. Markov property, where motivation and general definitions are given and detailed treatment of the Markov property is done; 2. Regular Markov processes, where regularity of the paths is studied; 3. Diffusion processes, with the investigation of connections with the partial differential equations and stochastic differential equations; 4. Homogeneous Markov processes, containing semigroups, strong Markov property, jumps, multiplicative and additive functionals, local structure of continuous processes; 5. Ergodic theory, with LLN type theorems, limits for transition probabilities.
We have almost got accustomed to thick books on the subject. This one is compact and capacious together. So, besides the evident theoretical value it may have an interest as a good base for any university course on Markov processes.

MSC:
60Jxx Markov processes
60-02 Research exposition (monographs, survey articles) pertaining to probability theory