Stable cylindrical Lévy processes and the stochastic Cauchy problem

2018/05/01 by Riedle, Markus
#47D06 #60G20 #60G52 #60H15 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1805.00278

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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