A Numerical scheme for backward doubly stochastic differential equations

Auguste Aman

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arXiv · 1011.6170

A Numerical scheme for backward doubly stochastic differential equations

Auguste Aman

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Abstract

In this paper we propose a numerical scheme for the class of backward doubly stochastic (BDSDEs) with possible path-dependent terminal values. We prove that our scheme converge in the strong $L^2$-sense and derive 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 though of as the modulus of continuity of the paths in an $L^2$-sense, is new.

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Auguste Aman. 2010-11-29. A Numerical scheme for backward doubly stochastic differential equations. https://arxiv.org/abs/1011.6170

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