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Description
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
Spécifications
Parties prenantes
- Auteur(s) :
- Editeur:
Contenu
- Nombre de pages :
- 448
- Langue:
- Anglais
- Collection :
- Tome:
- n° 38
Caractéristiques
- EAN:
- 9783110250107
- Date de parution :
- 17-03-11
- Format:
- Livre relié
- Format numérique:
- Genaaid
- Dimensions :
- 175 mm x 244 mm
- Poids :
- 884 g
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