Electronic Journal of Probability
- Electron. J. Probab.
- Volume 17 (2012), paper no. 27, 30 pp.
One-dimensional parabolic diffraction equations: pointwise estimates and discretization of related stochastic differential equations with weighted local times
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.
Electron. J. Probab., Volume 17 (2012), paper no. 27, 30 pp.
Accepted: 29 March 2012
First available in Project Euclid: 4 June 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60H10: Stochastic ordinary differential equations [See also 34F05]
This work is licensed under aCreative Commons Attribution 3.0 License.
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