Enrico Priola, Jerzy Zabczyk
Published 2009-08-03Version 1
We study an infinite-dimensional Ornstein-Uhlenbeck process $(X_t)$ in a given Hilbert space $H$. This is driven by a cylindrical symmetric L\'evy process without a Gaussian component and taking values in a Hilbert space $U$ which usually contains $H$. We give if and only if conditions under which $X_t$ takes values in $H$ for some $t>0$ or for all $t>0$. Moreover, we prove irreducibility for $(X_t)$.
Regularizing properties of (non-Gaussian) transition semigroups in Hilbert spaces
Scaling Limits of Solutions of Linear Evolution Equations with Random Initial Conditions
Fractional powers of monotone operators in Hilbert spaces
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