Continuous Weak Approximation for Stochastic Differential Equations

Kristian Debrabant; Andreas Rößler

doi:10.1016/j.cam.2007.02.040

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arXiv · 1303.4223

Continuous Weak Approximation for Stochastic Differential Equations

Kristian Debrabant·Andreas Rößler

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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.

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Kristian Debrabant, Andreas Rößler. 2013-03-18. Continuous Weak Approximation for Stochastic Differential Equations. https://doi.org/10.1016/j.cam.2007.02.040

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