Abstract
In this paper we consider the cylindrical càdlàg property of a solution to a linear equation in a Hilbert space H, driven by a Levy process taking values in a possibly larger Hilbert space U. In particular, we are interested in diagonal type processes, where processes on coordinates are functionals of independent α-stable symmetric processes. We give the equivalent characterization in this case. We apply the same techniques to obtain a sufficient condition for existence of a càdlàg version of stable processes described as integrals of deterministic functions with respect to symmetric α-stable random measures with .
Funding Statement
Research supported in part by National Science Centre, Poland, grant 2016/23/B/ST1/00492.
Research supported in part by National Science Centre, Poland, grant 2016/21/B/ST1/01489.
Acknowledgments
We are grateful to Martin Hairer who provided a nice MR macro and to Sébastien Gouëzel for his useful comments on the internals of the class file.
Citation
Witold Bednorz. Grzegorz Głowienko. Anna Talarczyk. "Time regularity of Lévy-type evolution in Hilbert spaces and of some α-stable processes.." Electron. Commun. Probab. 26 1 - 13, 2021. https://doi.org/10.1214/21-ECP403
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