A Numerical scheme for backward doubly stochastic differential equations

Auguste Aman

A Numerical scheme for backward doubly stochastic differential equations

Probability 2011-08-04 v2

Authors: Auguste Aman

Abstract

In this paper we propose a numerical scheme for the class of backward doubly stochastic (BDSDEs) with possible path-dependent terminal values. We prove that our scheme converge in the strong $L^2$ -sense and derive its rate of convergence. As an intermediate step we derive an $L^2$ -type regularity of the solution to such BDSDEs. Such a notion of regularity which can be though of as the modulus of continuity of the paths in an $L^2$ -sense, is new.

Keywords

backward stochastic differential equations stochastic differential equations reflected backward stochastic differential equations

Cite

@article{arxiv.1011.6170,
  title  = {A Numerical scheme for backward doubly stochastic differential equations},
  author = {Auguste Aman},
  journal= {arXiv preprint arXiv:1011.6170},
  year   = {2011}
}

Comments

The version has been greatly improved and is accepted for publication in Bernoulli

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