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arXiv · 2109.15208

Rate-independent stochastic evolution equations: parametrized solutions

Luca Scarpa·Ulisse Stefanelli
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Abstract

By extending to the stochastic setting the classical vanishing viscosity approach we prove the existence of suitably weak solutions of a class of nonlinear stochastic evolution equation of rate-independent type. Approximate solutions are obtained via viscous regularization. Upon properly rescaling time, these approximations converge to a parametrized martingale solution of the problem in rescaled time, where the rescaled noise is given by a general square-integrable cylindrical martingale with absolutely continuous quadratic variation. In absence of jumps, these are strong-in-time martingale solutions of the problem in the original, not rescaled time.

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Luca Scarpa, Ulisse Stefanelli. 2021-09-30. Rate-independent stochastic evolution equations: parametrized solutions. https://arxiv.org/abs/2109.15208

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