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.
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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.
Imprint | Scuola Normale Superiore |
Country of origin | Italy |
Series | Theses (Scuola Normale Superiore), 10 |
Release date | December 2008 |
Availability | Expected to ship within 12 - 17 working days |
First published | 2009 |
Authors | Luigi Manca |
Dimensions | 240 x 150 x 13mm (L x W x T) |
Format | Paperback |
Pages | 130 |
ISBN-13 | 978-88-7642-336-9 |
Barcode | 9788876423369 |
Categories | |
LSN | 88-7642-336-2 |