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.
General
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