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

2012/05/26 by Carlo Marinelli, Marinelli, Carlo, Luca Di Persio +3
Economics, Econometrics and Finance · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Biology Tumor Growth #Nonlinear Differential Equations Analysis #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1205.5875

openalex publication_date 2012/05/26 · openalex created_date 2022/09/26 · openalex updated_date 2026/07/28

Abstract

We prove that the mild solution to a semilinear stochastic evolution equation\non a Hilbert space, driven by either a square integrable martingale or a\nPoisson random measure, is (jointly) continuous, in a suitable topology, with\nrespect to the initial datum and all coefficients. In particular, if the\nleading linear operators are maximal (quasi-)monotone and converge in the\nstrong resolvent sense, the drift and diffusion coefficients are uniformly\nLipschitz continuous and converge pointwise, and the initial data converge,\nthen the solutions converge.\n

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