A weak second-order split-step method for numerical simulations of stochastic differential equations
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Date
2014-09
Publication Type
Journal Article
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yes
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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.
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published
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Journal / series
Volume
54 (3)
Pages / Article No.
801 - 821
Publisher
Springer
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Subject
Monte-Carlo; Stochastic differential equations; Stability
Organisational unit
03632 - Hiptmair, Ralf / Hiptmair, Ralf
Notes
It was possible to publish this article open access thanks to a Swiss National Licence with the publisher.