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

Étoré Pierre () and Martinez Miguel ()
Additional contact information
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

Monte Carlo Methods and Applications, 2013, vol. 19, issue 1, 41-71

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.

Keywords: Exact simulation methods; skew Brownian motion; one-dimensional diffusion; local time (search for similar items in EconPapers)
Date: 2013
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1515/mcma-2013-0002 (text/html)
For access to full text, subscription to the journal or payment for the individual article is required.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bpj:mcmeap:v:19:y:2013:i:1:p:41-71:n:3

Ordering information: This journal article can be ordered from
https://www.degruyter.com/journal/key/mcma/html

DOI: 10.1515/mcma-2013-0002

Access Statistics for this article

Monte Carlo Methods and Applications is currently edited by Karl K. Sabelfeld

More articles in Monte Carlo Methods and Applications from De Gruyter
Bibliographic data for series maintained by Peter Golla ().