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.
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}
}