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Exact simulation of one-dimensional stochastic differential equations involving the local time at zero of the unknown process

Author

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  • Étoré Pierre

    (Laboratoire Jean Kuntzmann, Tour IRMA 51, rue des Mathématiques, 38041 Grenoble Cedex 9, France)

  • Martinez Miguel

    (Laboratoire d'Analyse et de Mathématiques Appliquées, Université Paris-Est, UMR 8050, 5 Bld Descartes, Champs-sur-marne, 77454 Marne-la-Vallée Cedex 2, France)

Abstract

In this article we extend the exact simulation methods of Beskos, Papaspiliopoulos and Roberts [Bernoulli 12 (2006), 1077–1098] to the solutions of one-dimensional stochastic differential equations involving the local time of the unknown process at point zero. In order to perform the method we compute the law of the skew Brownian motion with drift. The method presented in this article covers the case where the solution of the SDE with local time corresponds to a divergence form operator with a discontinuous coefficient at zero. Numerical examples are shown to illustrate the method and the performances are compared with more traditional discretization schemes.

Suggested Citation

  • Étoré Pierre & Martinez Miguel, 2013. "Exact simulation of one-dimensional stochastic differential equations involving the local time at zero of the unknown process," Monte Carlo Methods and Applications, De Gruyter, vol. 19(1), pages 41-71, March.
    • Handle: RePEc:bpj:mcmeap:v:19:y:2013:i:1:p:41-71:n:3
    DOI: 10.1515/mcma-2013-0002
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    References listed on IDEAS

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    1. Alexandros Beskos & Omiros Papaspiliopoulos & Gareth O. Roberts, 2008. "A Factorisation of Diffusion Measure and Finite Sample Path Constructions," Methodology and Computing in Applied Probability, Springer, vol. 10(1), pages 85-104, March.
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