Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

Transition semigroups corresponding to Lipschitz dissipative systems

Pages: 177 - 192, Volume 10, Issue 1/2, January/February 2004      doi:10.3934/dcds.2004.10.177

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Giuseppe Da Prato - Scuola Normale Superiore di Pisa, Piazza dei Cavalieri 7, 56126, Pisa, Italy (email)

Abstract: We consider a semilinear differential stochastic equation in a Hilbert space $H$ with a dissipative and Lipschitz nonlinearity. We study the corresponding transition semigroup in a space $L^2(H,\nu)$ where $\nu$ is an invariant measure.

Keywords:  Markov semigroups, transition semigroups, dissipative systems, Lipschitz nonlinearities, Stochastic differential equations.
Mathematics Subject Classification:  47D07, 35K90, 60H15, 47B44.

Received: July 2001;      Revised: February 2002;      Available Online: October 2003.