Weak Convergence of Finite Element Approximations of Linear Stochastic Evolution Equations with Additive Lévy Noise

DOI10.1137/15M1009792zbMath1335.60131arXiv1411.1051OpenAlexW3021379411WikidataQ60580276 ScholiaQ60580276MaRDI QIDQ2801320

Mihály Kovács, Rene L. Schilling, Felix Lindner

Publication date: 6 April 2016

Published in: SIAM/ASA Journal on Uncertainty Quantification (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1411.1051

zbMATH Keywords

weak convergenceerror estimatesstochastic partial differential equationsfinite element approximationsstochastic Volterra integro-differential equationsPoisson random measurebackward Kolmogorov equationadditive Lévy noise

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Central limit and other weak theorems (60F05) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Random measures (60G57) PDEs with randomness, stochastic partial differential equations (35R60) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55) Stochastic integral equations (60H20)

Related Items (9)

Weak convergence rates for spatial spectral Galerkin approximations of semilinear stochastic wave equations with multiplicative noise ⋮ Lévy-driven Volterra equations in space and time ⋮ Some approximation results for mild solutions of stochastic fractional order evolution equations driven by Gaussian noise ⋮ Convergence of weak Euler approximation for nondegenerate stochastic differential equations driven by point and martingale measures ⋮ Weak convergence rates for stochastic evolution equations and applications to nonlinear stochastic wave, HJMM, stochastic Schrödinger and linearized stochastic Korteweg-de Vries equations ⋮ Monte Carlo versus multilevel Monte Carlo in weak error simulations of SPDE approximations ⋮ Weak convergence of Galerkin approximations of stochastic partial differential equations driven by additive Lévy noise ⋮ Weak convergence of fully discrete finite element approximations of semilinear hyperbolic SPDE with additive noise ⋮ Global solutions to stochastic Volterra equations driven by Lévy noise

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