BIT Numerical Mathematics

, Volume 54, Issue 3, pp 801–821 | Cite as

A weak second-order split-step method for numerical simulations of stochastic differential equations

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Abstract

In an analogy from symmetric ordinary differential equation numerical integrators, we derive a three-stage, weak 2nd-order procedure for Monte-Carlo simulations of Itô stochastic differential equations. Our composite procedure splits each time step into three parts: an \(h/2\)-stage of trapezoidal rule, an \(h\)-stage martingale, followed by another \(h/2\)-stage of trapezoidal rule. In \(n\) time steps, an \(h/2\)-stage deterministic step follows another \(n-1\) times. Each of these adjacent pairs may be combined into a single \(h\)-stage, effectively producing a two-stage method with partial overlap between successive time steps.

Keywords

Monte-Carlo Stochastic differential equations Stability 

Mathematics Subject Classification (2010)

34F05 65C05 65C30 
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Notes

Acknowledgments

We are grateful to our most critical reviewer. His/her hard work helped improve this paper significantly.

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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Seminar for Applied MathematicsETH ZürichZürichSwitzerland

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