Kolmogorov Operators in Spaces of Continuous Functions and Equations for Measures
Language: English
Published by Scuola Normale Superiore Dez 2008, 2008
- Softcover
- New
Seller: AHA-BUCH GmbH, Einbeck, GermanyAHA-BUCH GmbH
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Neuware - The book is devoted to study the relationships between Stochastic Partial Differential Equations and the associated Kolmogorov operator in spaces of continuous functions. In the first part, the theory of a weak convergence of functions is developed in order to give general results about Markov semigroups and their generator.In the second part, concrete models of Markov semigroups deriving from Stochastic PDEs are studied. In particular, Ornstein-Uhlenbeck, reaction-diffusion and Burgers equations have been considered. For each case the transition semigroup and its infinitesimal generator have been investigated in a suitable space of continuous functions.The main results show that the set of exponential functions provides a core for the Kolmogorov operator. As a consequence, the uniqueness of the Kolmogorov equation for measures has been proved.
Seller Inventory # 9788876423369
- Title
- Kolmogorov Operators in Spaces of Continuous Functions and Equations for Measures
- Author
- Luigi Manca
- Publisher
- Scuola Normale Superiore Dez 2008
- Publication year
- 2008
- Condition
- Neu
- Binding
- Taschenbuch
- Language
- English
- ISBN 10
- 8876423362
- ISBN 13
- 9788876423369
- Item weight
- 318 grams
- Dimensions
- 239x152x13 mm
The book is devoted to study the relationships between Stochastic Partial Differential Equations and the associated Kolmogorov operator in spaces of continuous functions.
In the first part, the theory of a weak convergence of functions is developed in order to give general results about Markov semigroups and their generator.
In the second part, concrete models of Markov semigroups deriving from Stochastic PDEs are studied. In particular, Ornstein-Uhlenbeck, reaction-diffusion and Burgers equations have been considered. For each case the transition semigroup and its infinitesimal generator have been investigated in a suitable space of continuous functions.
The main results show that the set of exponential functions provides a core for the Kolmogorov operator. As a consequence, the uniqueness of the Kolmogorov equation for measures has been proved.
"Synopsis" may belong to another edition of this title.
Review
From the reviews:
“This volume of the Edizioni Della Normale is based on the authors’s thesis about the relationship of the solutions of a class stochastic partial differential equations (SPDE) with additive noise, the associated Kolmogorov operator and the associated Markov generator on spaces of continuous functions. ... This monography gives a nice introduction to the field of measure valued Kolmogorov equations for a quite general class SPDE.” (Michael Högele, Zentralblatt MATH, Vol. 1198, 2010)"About the title" may belong to another edition of this title.
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