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February 2013 A numerical scheme for backward doubly stochastic differential equations
Auguste Aman
Bernoulli 19(1): 93-114 (February 2013). DOI: 10.3150/11-BEJ391

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.

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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

Information

Published: February 2013
First available in Project Euclid: 18 January 2013

zbMATH: 1274.60217
MathSciNet: MR3019487
Digital Object Identifier: 10.3150/11-BEJ391

Keywords: $L^{\infty}$-Lipschitz functionals , $L^{2}$-regularity , Backward doubly SDEs , Numerical scheme , Regression estimation

Rights: Copyright © 2013 Bernoulli Society for Mathematical Statistics and Probability

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Vol.19 • No. 1 • February 2013
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