We study the Cauchy problem for a class of Markov-type semigroups (not strongly continuous in general) in the space of all real, uniformly continuous and bounded functions on a separable metric space. In this class there are many transition Markov semigroups corresponding to stochastic differential equations in infinite dimensions as the heat semigroup and the one of Ornstein-Uhlenbeck. We define appropriate notions of solution and give existence and uniqueness theorems. Additional regularity results about the Cauchy problem associated with the Ornstein-Uhlenbeck semigroup are also proved.
The Cauchy problem for a class of Markov-type semigroups
E. Priola
2001-01-01
Abstract
We study the Cauchy problem for a class of Markov-type semigroups (not strongly continuous in general) in the space of all real, uniformly continuous and bounded functions on a separable metric space. In this class there are many transition Markov semigroups corresponding to stochastic differential equations in infinite dimensions as the heat semigroup and the one of Ornstein-Uhlenbeck. We define appropriate notions of solution and give existence and uniqueness theorems. Additional regularity results about the Cauchy problem associated with the Ornstein-Uhlenbeck semigroup are also proved.File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
