Continuous Parameter Markov Processes and Stochastic Differential Equations
Language: English
Published by Springer International Publishing, 2023
- Hardcover
- New
Condition: New
£ 70.11
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Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Builds from simple examples to formal proofs, illuminating key ideas and computationsMarkov processes has an elegant and profound mathematical theory and a great diversity of applicationsSet of course suggestions and a chapter dependency di.
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- Title
- Continuous Parameter Markov Processes and Stochastic Differential Equations
- Author
- Rabi Bhattacharya|Edward C. Waymire
- Publisher
- Springer International Publishing
- Publication year
- 2023
- Condition
- New
- Binding
- Hardcover
- Language
- English
- ISBN 10
- 3031332946
- ISBN 13
- 9783031332944
This graduate text presents the elegant and profound theory of continuous parameter Markov processes and many of its applications. The authors focus on developing context and intuition before formalizing the theory of each topic, illustrated with examples.
After a review of some background material, the reader is introduced to semigroup theory, including the Hille–Yosida Theorem, used to construct continuous parameter Markov processes. Illustrated with examples, it is a cornerstone of Feller’s seminal theory of the most general one-dimensional diffusions studied in a later chapter. This is followed by two chapters with probabilistic constructions of jump Markov processes, and processes with independent increments, or Lévy processes. The greater part of the book is devoted to Itô’s fascinating theory of stochastic differential equations, and to the study of asymptotic properties of diffusions in all dimensions, such as explosion, transience, recurrence, existence of steady states, and the speed of convergence to equilibrium. A broadly applicable functional central limit theorem for ergodic Markov processes is presented with important examples. Intimate connections between diffusions and linear second order elliptic and parabolic partial differential equations are laid out in two chapters, and are used for computational purposes. Among Special Topics chapters, two study anomalous diffusions: one on skew Brownian motion, and the other on an intriguing multi-phase homogenization of solute transport in porous media.
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