Perturbation of Ornstein-Uhlenbeck semigroups
Perturbation of Ornstein-Uhlenbeck semigroups
Consider the following stochastic equation in a Hilbert space \(dZ=AZ dt+ dW(t)\) with \(Z(0)=x\), where \(W\) is a cylindrical Wiener process. The main result of the paper is a precise characterization of the domain \(D\) of the infinitesimal generator of the transition semigroup \(R_t\varphi(x)= E(\varphi(Z(t,x)))\). The domain \(D\) is considered as a subspace of \(W^{2,2}(H;\mu)\), where \(\mu\) is a unique invariant measure of the process \(Z(t,x)\).
- University of Trieste Italy
Stochastic partial differential equations (aspects of stochastic analysis), stochastic partial differential equations, transition semigroup, cylindrical Wiener process, Ornstein-Uhlenbeck process
Stochastic partial differential equations (aspects of stochastic analysis), stochastic partial differential equations, transition semigroup, cylindrical Wiener process, Ornstein-Uhlenbeck process
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