English

The asymptotic error of chaos expansion approximations for stochastic differential equations

Probability 2019-06-05 v1

Abstract

In this paper we present a numerical scheme for stochastic differential equations based upon the Wiener chaos expansion. The approximation of a square integrable stochastic differential equation is obtained by cutting off the infinite chaos expansion in chaos order and in number of basis elements. We derive an explicit upper bound for the L2L^2 approximation error associated with our method. The proofs are based upon an application of Malliavin calculus.

Keywords

Cite

@article{arxiv.1906.01209,
  title  = {The asymptotic error of chaos expansion approximations for stochastic differential equations},
  author = {Tony Huschto and Mark Podolskij and Sebastian Sager},
  journal= {arXiv preprint arXiv:1906.01209},
  year   = {2019}
}

Comments

Published at https://doi.org/10.15559/19-VMSTA133 in the Modern Stochastics: Theory and Applications (https://vmsta.org/) by VTeX (http://www.vtex.lt/)