Geiss, Christel; Labart, Céline; Luoto, Antti Random walk approximation of BSDEs with Hölder continuous terminal condition. (English) Zbl 1433.60033 Bernoulli 26, No. 1, 159-190 (2020). Summary: In this paper, we consider the random walk approximation of the solution of a Markovian BSDE whose terminal condition is a locally Hölder continuous function of the Brownian motion. We state the rate of the \(L_2\)-convergence of the approximated solution to the true one. The proof relies in part on growth and smoothness properties of the solution \(u\) of the associated PDE. Here we improve existing results by showing some properties of the second derivative of \(u\) in space. Cited in 7 Documents MSC: 60H10 Stochastic ordinary differential equations (aspects of stochastic analysis) 65C30 Numerical solutions to stochastic differential and integral equations 60H30 Applications of stochastic analysis (to PDEs, etc.) 65C05 Monte Carlo methods Keywords:backward stochastic differential equations; numerical scheme; random walk approximation; speed of convergence × Cite Format Result Cite Review PDF Full Text: DOI arXiv Euclid References: [1] Alanko, S. (2015). Regression-based Monte Carlo methods for solving nonlinear PDEs. Ph.D. thesis, New York University. · Zbl 1337.65009 · doi:10.1002/cpa.21590 [2] Bally, V. (1997). Approximation scheme for solutions of BSDE. In Backward Stochastic Differential Equations (Paris, 1995-1996). Pitman Res. Notes Math. Ser. 364 177-191. Harlow: Longman. · Zbl 0889.60068 [3] Bally, V. and Pagès, G. (2003). A quantization algorithm for solving multi-dimensional discrete-time optimal stopping problems. 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