Some approximation results for mild solutions of stochastic fractional order evolution equations driven by Gaussian noise

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• Mihaly Kovacs (Pázmány Péter Catholic University, Chalmers University of Technology)
• Tuesday 22 February 2022, 09:30-10:00
• Seminar Room 1, Newton Institute.

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FD2W01 - Deterministic and stochastic fractional differential equations and jump processes

We investigate the quality of space approximations of a class of stochastic integral equations of convolution type with Gaussian noise. Such equations arise, for example, when considering mild solutions of stochastic fractional order partial differential equations but also when considering mild solutions of classical stochastic partial differential equations. The key requirement for the equations is a smoothing property of the deterministic evolution operator which is typical in parabolic type problems. We show that if one has access to nonsmooth data estimates for the deterministic error operator together with its derivative of a space discretization procedure, then one obtains error estimates in pathwise H\”older norms with rates that can be read off the deterministic error rates. This is a joint work with Erika Hausenblas (Montanuniversität Leoben) and Kistosil Fahim (Institut Teknologi Sepuluh Nopember).

This talk is part of the Isaac Newton Institute Seminar Series series.

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