Abstract
In this paper we propose a numerical scheme for the class of backward doubly stochastic differential equations (BDSDEs) with possible path-dependent terminal values. We prove that our scheme converges in the strong $L^{2}$-sense and derives its rate of convergence. As an intermediate step we derive an $L^{2}$-type regularity of the solution to such BDSDEs. Such a notion of regularity, which can be thought of as the modulus of continuity of the paths in an $L^{2}$-sense, is new.
Citation
Auguste Aman. "A numerical scheme for backward doubly stochastic differential equations." Bernoulli 19 (1) 93 - 114, February 2013. https://doi.org/10.3150/11-BEJ391
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