Markov Processes, Semigroups and Generators

ISBN-13: 9783110250107 / Angielski / Twarda / 2011 / 448 str.

V. N. (Vasilii Nikitich) Kolokoltsov

Opis

This work offers a highly useful, well developed reference on Markov processes, the universal model for random processes and evolutions. The wide range of applications, in exact sciences as well as in other areas like social studies, require a volume that offers a refresher on fundamentals before conveying the Markov processes and examples for applications. This work does just that, and with the necessary mathematical rigor.

Recenzje

"[...] As a whole, the book is a valuable source of information both for specialists in the field and those who study the theory of stochastic processes."
Anatoly N. Kochubei, Zentralblatt für Mathematik

Spis treści

Part I Brownian Motion, Markov Processes, Martingales.

1 Preliminaries in Probability and Analysis.

2 Browninan Motion I: Constructions.

3 Martingales and Markov Processes.

4 Browninan Motion II: Elements of Analysis.

Part II Basic Constructions of Markov Semigroups.

1 Analytic Constructions.

2 Probabilistic Constructions.

3 Heat Kernel Estimates.

4 Process in Cones and Bounded Domains.

Part III Extensions, Developments, Applications.

1 CTRW and Fractional Dynamics.

2 Complex Markov Chains and Feynman integral.

3 Controlled Processes.

4 Semiclassical Asymptotic.

5 Miscellany.

6 Bibliographical Comments.

O autorze

Vassili N. Kolokoltsov, University of Warwick, UK.