BIRS Workshop Lecture Videos
Time regularity of solutions to SPDEs Peszat, Szymon
Time regularity of solutions to SPDEs driven by Wiener process can be studied using either Kolmogorov criterion, Kotelenez theorem or Da Prato-Kwapien ́-Zabczyk factorization. It turns out that very often the solution is continuous is a given state space E even if the noise takes values in a bigger space U - E. If the noise is of jump type and does not take values in the space space then typically the solution is not c`adl`ag. In fact during the talk di↵erent concepts of c`adl`ag property will be discussed. A special emphasis will be put on infinite systems of linear equations driven by independent L ́evy processes. The talk will be based on the following papers: • S. Peszat and J. Zabczyk, Time regularity for stochastic Volterra equations by the dilation theorem, J. Math. Anal. Appl. 409 (2014), 676–683. • S. Peszat and J. Zabczyk, Time regularity of solutions to linear equations with L ́evy noise in infinite dimensions, Stochastic Processes Appl. 123 (2013), 719–751. • Z. Brze ́zniak, B. Goldys, P. Imkeller, S. Peszat, E. Priola, and J. Zabczyk, Time irregularity of generalized Ornstein–Uhlenbeck processes, C. R. Math. Acad. Sci. Paris 348 (2010), 273–276.
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