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Unbiased simulation of stochastic differential equations using parametrix expansions
Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Statistics.
2017 (English)In: Bernoulli, ISSN 1350-7265, E-ISSN 1573-9759, Vol. 23, no 3, p. 2028-2057Article in journal (Refereed) Published
Abstract [en]

In this article, we consider an unbiased simulation method for multidimensional diffusions based on the parametrix method for solving partial differential equations with Holder continuous coefficients. This Monte Carlo method which is based on an Euler scheme with random time steps, can be considered as an infinite dimensional extension of the Multilevel Monte Carlo method for solutions of stochastic differential equations with Holder continuous coefficients. In particular, we study the properties of the variance of the proposed method. In most cases, the method has infinite variance and therefore we propose an importance sampling method to resolve this issue.

Place, publisher, year, edition, pages
2017. Vol. 23, no 3, p. 2028-2057
Keywords [en]
importance sampling, Monte Carlo method, multidimensional diffusion, parametrix
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:uu:diva-287356DOI: 10.3150/16-BEJ803ISI: 000398013100019OAI: oai:DiVA.org:uu-287356DiVA, id: diva2:922635
Funder
Swedish Research CouncilAvailable from: 2016-04-24 Created: 2016-04-24 Last updated: 2017-05-12Bibliographically approved

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Andersson, Patrik

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