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Stable cylindrical Lévy processes and the stochastic Cauchy problem

Research output: Contribution to journalArticle

Original languageEnglish
Article number36
Number of pages12
JournalElectronic Communications in Probability
Volume23
Early online date7 Jun 2018
DOIs
Accepted/In press26 Apr 2018
E-pub ahead of print7 Jun 2018

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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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