Stable cylindrical Lévy processes and the stochastic Cauchy problem

Markus Riedle

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arXiv · 1805.00278

Stable cylindrical Lévy processes and the stochastic Cauchy problem

Markus Riedle

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Abstract

In this work, we consider the stochastic Cauchy problem driven by the canonical $α$-stable cylindrical Lévy process. This noise naturally generalises the cylindrical Brownian motion or space-time Gaussian white noise. We derive a sufficient and necessary condition for the existence of the weak and mild solution of the stochastic Cauchy problem and establish the temporal irregularity of the solution.

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Markus Riedle. 2018-05-01. Stable cylindrical Lévy processes and the stochastic Cauchy problem. https://arxiv.org/abs/1805.00278

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