English

Continuous Weak Approximation for Stochastic Differential Equations

Numerical Analysis 2013-03-19 v1

Abstract

A convergence theorem for the continuous weak approximation of the solution of stochastic differential equations by general one step methods is proved, which is an extension of a theorem due to Milstein. As an application, uniform second order conditions for a class of continuous stochastic Runge-Kutta methods containing the continuous extension of the second order stochastic Runge-Kutta scheme due to Platen are derived. Further, some coefficients for optimal continuous schemes applicable to It\^o stochastic differential equations with respect to a multi-dimensional Wiener process are presented.

Keywords

Cite

@article{arxiv.1303.4223,
  title  = {Continuous Weak Approximation for Stochastic Differential Equations},
  author = {Kristian Debrabant and Andreas Rößler},
  journal= {arXiv preprint arXiv:1303.4223},
  year   = {2013}
}
R2 v1 2026-06-21T23:43:39.752Z