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arXiv · 0908.0356

On linear evolution equations with cylindrical Lévy noise

Enrico Priola·Jerzy Zabczyk
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Abstract

We study an infinite-dimensional Ornstein-Uhlenbeck process $(X_t)$ in a given Hilbert space $H$. This is driven by a cylindrical symmetric Lévy 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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Enrico Priola, Jerzy Zabczyk. 2009-08-03. On linear evolution equations with cylindrical Lévy noise. https://arxiv.org/abs/0908.0356

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