A Numerical scheme for backward doubly stochastic differential equations

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 regularit...

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Bibliographic Details
Published in:arXiv.org 2011-08
Main Author: Auguste Aman
Format: Article
Language:English
Subjects:
Convergence
Differential equations
Economic models
Regularity
Online Access:Get full text
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Summary: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.
ISSN:2331-8422