Mean square rate of convergence for random walk approximation of forward-backward SDEs

• Published in: Advances in applied probability Vol. 52; no. 3; pp. 735 - 771
• Main Authors: Geiss, Christel, Labart, Céline, Luoto, Antti
• Format: Journal Article
• Language: English
• Published: Cambridge, UK Cambridge University Press 01.09.2020; Applied Probability Trust
• Subjects: Approximation; Brownian motion; Convergence; Difference equations; Differential calculus; Finite difference method; Mathematical analysis; Mathematics; Original Article; Original Articles; Partial differential equations; Probabilistic methods; Probability; Properties (attributes); Random variables; Random walk; Smoothness; Backward stochastic differential equations; 60H10; 60H30; 60G50; finite difference equation; random walk approximation; approximation scheme; convergence rate; 60H35; random walk approximation 2010 Mathematics Subject Classification: Primary 60H10; 60G50 Secondary 60H30

Let (Y, Z) denote the solution to a forward-backward stochastic differential equation (FBSDE). If one constructs a random walk $B^n$ from the underlying Brownian motion B by Skorokhod embedding, one can show $L_2$-convergence of the corresponding solutions $(Y^n,Z^n)$ to $(Y, Z).$ We estimate the ra...