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arXiv · 1205.5875

Approximation and convergence of solutions to semilinear stochastic evolution equations with jumps

Carlo Marinelli·Luca Di Persio·Giacomo Ziglio
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Abstract

We prove that the mild solution to a semilinear stochastic evolution equation on a Hilbert space, driven by either a square integrable martingale or a Poisson random measure, is (jointly) continuous, in a suitable topology, with respect to the initial datum and all coefficients. In particular, if the leading linear operators are maximal (quasi-)monotone and converge in the strong resolvent sense, the drift and diffusion coefficients are uniformly Lipschitz continuous and converge pointwise, and the initial data converge, then the solutions converge.

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Carlo Marinelli, Luca Di Persio, Giacomo Ziglio. 2012-05-26. Approximation and convergence of solutions to semilinear stochastic evolution equations with jumps. https://arxiv.org/abs/1205.5875

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