Kolmogorov operators in spaces of continuous functions and equations for measures

著者

• Manca, Luigi

書誌事項

Kolmogorov operators in spaces of continuous functions and equations for measures

Luigi Manca

（Tesi = theses, 10）

Edizioni della Normale, Scuola Normale Superiore, c2008

注記

Includes bibliographical references (p. [119]-122) and index

内容説明・目次

内容説明

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.

目次

1. Introduction.- 2. Preliminaries.- 3. Measure valued equations for stochastically continuous Markov semigroups.- 4. Measure equations for Ornstein-Uhlenbeck operators.- 5. Bounded perturbations of Ornstein-Uhlenbeck operators.- 6. Lipschitz perturbations of Ornstein-Uhlenbeck operators.- 7. The reaction-diffusion operator.- 8. The Burgers equation.- Bibliography.- Index.

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詳細情報

• NII書誌ID(NCID): BA88949632
• ISBN:
  • 9788876423369
• 出版国コード: it
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Pisa
• ページ数/冊数: xiv, 127 p.
• 大きさ: 24 cm
• 件名:
  • LCSH : Stochastic partial differential equations
  • LCSH : Diffusion processes
• 親書誌ID:
  • BA86073952