Electronic Journal of Probability

One-dimensional parabolic diffraction equations: pointwise estimates and discretization of related stochastic differential equations with weighted local times

Miguel Martinez and Denis Talay

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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.

Article information

Electron. J. Probab., Volume 17 (2012), paper no. 27, 30 pp.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60H10: Stochastic ordinary differential equations [See also 34F05]
Secondary: 65U05

Stochastic Differential Equations Divergence Form Operators Euler discretization scheme Monte Carlo methods

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Martinez, Miguel; Talay, Denis. One-dimensional parabolic diffraction equations: pointwise estimates and discretization of related stochastic differential equations with weighted local times. Electron. J. Probab. 17 (2012), paper no. 27, 30 pp. doi:10.1214/EJP.v17-1905. https://projecteuclid.org/euclid.ejp/1465062349

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