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Exact sampling of diffusions with a discontinuity in the drift

Part of: Probabilistic methods, simulation and stochastic differential equations Stochastic analysis

Published online by Cambridge University Press:  25 July 2016

Omiros Papaspiliopoulos ,
Gareth O. Roberts  and
Kasia B. Taylor
Omiros Papaspiliopoulos*
Affiliation:
ICREA and Universitat Pompeu Fabra
Gareth O. Roberts*
Affiliation:
University of Warwick
Kasia B. Taylor*
Affiliation:
University of Warwick
*
Department of Economics and Business, Universitat Pompeu Fabra, Ramon Trias Fargas 25‒27, 08005 Barcelona, Spain. Email address: [email protected]
Department of Statistics, University of Warwick, Coventry, CV4 7AL, UK. Email address: [email protected]
Department of Statistics and Mathematics Institute, University of Warwick, Coventry, CV4 7AL, UK. Email address: [email protected]
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Abstract

We introduce exact methods for the simulation of sample paths of one-dimensional diffusions with a discontinuity in the drift function. Our procedures require the simulation of finite-dimensional candidate draws from probability laws related to those of Brownian motion and its local time, and are based on the principle of retrospective rejection sampling. A simple illustration is provided.

Keywords

Exact algorithmsampling of diffusionsdiffusion with discontinuous driftretrospective rejection sampling

MSC classification

Primary: 65C30: Stochastic differential and integral equations
Secondary: 60H35: Computational methods for stochastic equations 65C05: Monte Carlo methods
Type
Research Article
Information
Advances in Applied Probability , Volume 48 , Issue A: Probability, Analysis and Number Theory , July 2016 , pp. 249 - 259
Copyright
Copyright © Applied Probability Trust 2016 

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References

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