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2020 The stochastic Cauchy problem driven by a cylindrical Lévy process
Umesh Kumar, Markus Riedle
Electron. J. Probab. 25: 1-26 (2020). DOI: 10.1214/19-EJP407


In this work, we derive sufficient and necessary conditions for the existence of a weak and mild solution of an abstract stochastic Cauchy problem driven by an arbitrary cylindrical Lévy process. Our approach requires to establish a stochastic Fubini result for stochastic integrals with respect to cylindrical Lévy processes. This approach enables us to conclude that the solution process has almost surely scalarly square integrable paths. Further properties of the solution such as the Markov property and stochastic continuity are derived.


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Umesh Kumar. Markus Riedle. "The stochastic Cauchy problem driven by a cylindrical Lévy process." Electron. J. Probab. 25 1 - 26, 2020.


Received: 14 February 2019; Accepted: 22 December 2019; Published: 2020
First available in Project Euclid: 29 January 2020

zbMATH: 1445.60045
MathSciNet: MR4059188
Digital Object Identifier: 10.1214/19-EJP407

Primary: 60G20 , 60G51 , 60H05 , 60H15

Keywords: Cauchy problem , cylindrical infinitely divisible , cylindrical Lévy process , stochastic Fubini theorem


Vol.25 • 2020
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