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Kolmogorov Operators in Spaces of Continuous Functions and Equations for Measures

Luigi Manca 1
1 OPALE - Optimization and control, numerical algorithms and integration of complex multidiscipline systems governed by PDE
CRISAM - Inria Sophia Antipolis - Méditerranée , JAD - Laboratoire Jean Alexandre Dieudonné : UMR6621
Abstract : The thesis 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 (also called Fokker-Planck) has been proved.
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Contributor : Luigi Manca <>
Submitted on : Monday, April 27, 2009 - 11:42:33 AM
Last modification on : Monday, October 12, 2020 - 2:28:02 PM
Long-term archiving on: : Thursday, June 10, 2010 - 9:58:54 PM


  • HAL Id : tel-00378888, version 1



Luigi Manca. Kolmogorov Operators in Spaces of Continuous Functions and Equations for Measures. Mathematics [math]. Scuola Normale Superiore di Pisa, 2008. English. ⟨tel-00378888⟩



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