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

   
@article{EJP1905,
	author = {Miguel Martinez and Denis Talay},
	title = {One-dimensional parabolic diffraction equations: pointwise estimates and discretization of related stochastic differential equations with weighted local times},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {17},
	year = {2012},
	keywords = {Stochastic Differential Equations; Divergence Form Operators;  Euler discretization scheme; Monte Carlo methods},
	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.},
	pages = {no. 27, 1-30},
	issn = {1083-6489},
	doi = {10.1214/EJP.v17-1905},    
        url = {http://ejp.ejpecp.org/article/view/1905}}