1.

Record Nr.

UNINA9910828220403321

Autore

Kolokolʹt͡sov V. N (Vasiliĭ Nikitich)

Titolo

Markov processes, semigroups, and generators / / Vassili N. Kolokoltsov

Pubbl/distr/stampa

Berlin ; ; New York, : De Gruyter, c2011

ISBN

1-283-16633-X

9786613166333

3-11-025011-X

Edizione

[1st ed.]

Descrizione fisica

1 online resource (448 p.)

Collana

De Gruyter studies in mathematics, , 0179-0986 ; ; 38

Classificazione

SK 820

Disciplina

519.2/33

Soggetti

Markov processes

Semigroups

Group theory - Generators

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Description based upon print version of record.

Nota di bibliografia

Includes bibliographical references and index.

Nota di contenuto

pt. 1. Introduction to stochastic analysis -- pt. 2. Markov processes and beyond.

Sommario/riassunto

Markov processes represent a universal model for a large variety of real life random evolutions. The wide flow of new ideas, tools, methods and applications constantly pours into the ever-growing stream of research on Markov processes that rapidly spreads over new fields of natural and social sciences, creating new streamlined logical paths to its turbulent boundary. Even if a given process is not Markov, it can be often inserted into a larger Markov one (Markovianization procedure) by including the key historic parameters into the state space. This monograph gives a concise, but systematic and self-contained, exposition of the essentials of Markov processes, together with recent achievements, working from the "physical picture" - a formal pre-generator, and stressing the interplay between probabilistic (stochastic differential equations) and analytic (semigroups) tools. The book will be useful to students and researchers. Part I can be used for a one-semester course on Brownian motion, Lévy and Markov processes, or on probabilistic methods for PDE. Part II mainly contains the author's research on Markov processes. From the contents: Tools from



Probability and Analysis Brownian motion Markov processes and martingales SDE, ψDE and martingale problems Processes in Euclidean spaces Processes in domains with a boundary Heat kernels for stable-like processes Continuous-time random walks and fractional dynamics Complex chains and Feynman integral