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Session S17 - Stochastic Systems: Analysis, Numerics and Applications

Friday, July 16, 15:35 ~ 16:10 UTC-3

Stochastic Evolution Equations with Lévy Noise in Spaces of Distributions

Christian Fonseca-Mora

University of Costa Rica, Costa Rica   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

In the first part of this talk, I will give sufficient and necessary conditions for the existence of a weak and mild solution to a time-dependent linear stochastic evolution equation with linear Lévy noise taking values in the dual of a nuclear space (of which spaces of distributions are a particular example). We also derive further properties of the solution such as the existence of a solution with square moments, the Markov property and path regularity of the solution. Later we provide sufficient conditions for the weak convergence of the mild solutions to a sequence of linear stochastic evolution equations with Lévy noise.

We will end this talk by giving sufficient conditions for existence and uniqueness of weak and mild solutions to non-linear stochastic evolution equations driven by general multiplicative Lévy noise.

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