On linear evolution equations with cylindrical Lévy noise

Details On linear evolution equations with cylindrical Lévy noise On linear evolution equations with cylindrical Lévy noise

2009-08-03

arxiv.org/abs/0908.0356v1

Mathematics

Analysis of PDEs

Scientific paper

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 $(X_t)$.

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