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February  2004, 10(1&2): 177-192. doi: 10.3934/dcds.2004.10.177

Transition semigroups corresponding to Lipschitz dissipative systems

Giuseppe Da Prato 1,

1. 

Scuola Normale Superiore di Pisa, Piazza dei Cavalieri 7, 56126, Pisa, Italy

Received  July 2001 Revised  February 2002 Published  October 2003

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: dissipative systems, transition semigroups, Stochastic differential equations., Lipschitz nonlinearities, Markov semigroups.
Mathematics Subject Classification: 47D07, 35K90, 60H15, 47B4.
Citation: Giuseppe Da Prato. Transition semigroups corresponding to Lipschitz dissipative systems. Discrete and Continuous Dynamical Systems, 2004, 10 (1&2) : 177-192. doi: 10.3934/dcds.2004.10.177
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