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Markov semigroups and their applications. (English) Zbl 1057.47046
Garbaczewski, Piotr (ed.) et al., Dynamics of dissipation. Invited lectures delivered during the 38th Karpacz winter school of theoretical physics on “Dynamical semigroups: Dissipation, chaos, quanta”, Lądek Zdrój, Poland, February 6–15, 2002. Berlin: Springer (ISBN 3-540-44111-5/hbk). Lect. Notes Phys. 597, 215-238 (2002).
The paper is a survey on some recent results concerning the asymptotic properties of Markov operators and semigroups. Frobenius–Perron operators, stability, sweeping, Foguel alternative and other asymptotic properties are discussed. Applications to differential equations connected with diffusions and jump processes are illustrated. The main results are not proved here but can be found in the large list of references given.
For the entire collection see [Zbl 1030.00047].

MSC:
47D07 Markov semigroups and applications to diffusion processes
60J35 Transition functions, generators and resolvents
47A35 Ergodic theory of linear operators
60J70 Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)
47-02 Research exposition (monographs, survey articles) pertaining to operator theory
47N20 Applications of operator theory to differential and integral equations
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