Rate of Convergence of Space Time Approximations for Stochastic Evolution Equations

2007/06/30 by Istvan Gyöngy, István Gyöngy, Annie Millet · 59 citations
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #Banach space #Brownian motion #Class (philosophy) #Convergence (economics) #Geometric Brownian motion #Lipschitz continuity #Monotonic function #Nonlinear Differential Equations Analysis #Nonlinear system #Rate of convergence #Risk and Portfolio Optimization #Stochastic process #Stochastic processes and financial applications #math.PR #msc:60H15 #msc:65M60

paper · pdf · doi:10.1007/s11118-008-9105-5

published in Potential Analysis 30(1), 29-64 (Springer Science+Business Media) · 33 pages

arxiv created 2008/09/30 · openalex publication_date 2008/11/20 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

Stochastic evolution equations in Banach spaces with unbounded nonlinear drift and diffusion operators driven by a finite dimensional Brownian motion are considered. Under some regularity condition assumed for the solution, the rate of convergence of various numerical approximations are estimated under strong monotonicity and Lipschitz conditions. The abstract setting involves general consistency conditions and is then applied to a class of quasilinear stochastic PDEs of parabolic type.

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