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An interpolated stochastic algorithm for quasi-linear PDEs


Authors: François Delarue and Stéphane Menozzi
Journal: Math. Comp. 77 (2008), 125-158
MSC (2000): Primary 65C30; Secondary 60H10, 60H35
DOI: https://doi.org/10.1090/S0025-5718-07-02008-X
Published electronically: July 26, 2007
MathSciNet review: 2353946
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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, we improve the forward-backward algorithm for quasi-linear PDEs introduced in Delarue and Menozzi (2006). The new discretization scheme takes advantage of the standing regularity properties of the true solution through an interpolation procedure. For the convergence analysis, we also exploit the optimality of the square Gaussian quantization used to approximate the conditional expectations involved.

The resulting bound for the error is closely related to the Hölder exponent of the second order spatial derivatives of the true solution and turns out to be more satisfactory than the one previously established.


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Additional Information

François Delarue
Affiliation: Université Paris 7, UFR de Mathématiques, Case 7012, 2, Place Jussieu, 75251 Paris Cedex 05, France
Email: delarue@math.jussieu.fr

Stéphane Menozzi
Affiliation: Université Paris 7, UFR de Mathématiques, Case 7012, 2, Place Jussieu, 75251 Paris Cedex 05, France
Email: menozzi@math.jussieu.fr

DOI: https://doi.org/10.1090/S0025-5718-07-02008-X
Received by editor(s): March 30, 2006
Received by editor(s) in revised form: October 31, 2006
Published electronically: July 26, 2007
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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