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2012 One-dimensional parabolic diffraction equations: pointwise estimates and discretization of related stochastic differential equations with weighted local times
Miguel Martinez, Denis Talay
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Electron. J. Probab. 17: 1-30 (2012). DOI: 10.1214/EJP.v17-1905

Abstract

In this paper we consider one-dimensional partial differential equations of parabolic type involving a divergence form operator with a discontinuous coefficient and a compatibility transmission condition. We prove existence and uniqueness result by stochastic methods which also allow us to develop a low complexity Monte Carlo numerical resolution method. We get accurate pointwise estimates for the derivatives of the solutionfrom which we get sharp convergence rate estimates for our stochastic numerical method.

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Miguel Martinez. Denis Talay. "One-dimensional parabolic diffraction equations: pointwise estimates and discretization of related stochastic differential equations with weighted local times." Electron. J. Probab. 17 1 - 30, 2012. https://doi.org/10.1214/EJP.v17-1905

Information

Accepted: 29 March 2012; Published: 2012
First available in Project Euclid: 4 June 2016

zbMATH: 1244.60058
MathSciNet: MR2912504
Digital Object Identifier: 10.1214/EJP.v17-1905

Subjects:
Primary: 60H10
Secondary: 65U05

JOURNAL ARTICLE
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Vol.17 • 2012
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