A Semidiscrete Galerkin Scheme for Backward Stochastic Parabolic Differential Equations

2015/07/15 by Yanqing Wang, Wang, Yanqing
Earth and Planetary Sciences · Economics, Econometrics and Finance · Engineering · Mathematics · #60H15 #65M60 #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Meteorological Phenomena and Simulations #Optimization and Control (math.OC) #Stochastic processes and financial applications #math.OC #msc:60H15 #msc:65M60

paper · pdf · doi:10.48550/arxiv.1507.04100

25 pages

arxiv created 2015/07/15 · openalex publication_date 2015/07/15 · arxiv updated 2015/07/16 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

In this paper, we present a numerical scheme to solve the initial-boundary value problem for backward stochastic partial differential equations of parabolic type. Based on the Galerkin method, we approximate the original equation by a family of backward stochastic differential equations (BSDEs, for short), and then solve these BSDEs by the time discretization. Combining the truncation with respect to the spatial variable and the backward Euler method on time variable, we obtain the global L² error estimate.

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