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Integration by Parts for Point Processes and Monte Carlo Estimation

Part of: Nonparametric inference Stochastic analysis Stochastic processes Special processes Probabilistic methods, simulation and stochastic differential equations

Published online by Cambridge University Press:  14 July 2016

Nicolas Privault  and
Xiao Wei
Nicolas Privault
Affiliation:
Université de Poitiers
Xiao Wei*
Affiliation:
Central University of Finance and Economics
*
∗∗Postal address: School of Insurance, Central University of Finance and Economics, Beijing, 100081, P. R. China. Email address: [email protected]
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Abstract

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We develop an integration by parts technique for point processes, with application to the computation of sensitivities via Monte Carlo simulations in stochastic models with jumps. The method is applied to density estimation with respect to the Lebesgue measure via a modified kernel estimator which is less sensitive to variations of the bandwidth parameter than standard kernel estimators. This applies to random variables whose densities are not analytically known and requires the knowledge of the point process jump times.

Keywords

Malliavin calculuspoint processrenewal processsensitivity analysisdensity estimationkernel estimator

MSC classification

Secondary: 62G07: Density estimation 60H07: Stochastic calculus of variations and the Malliavin calculus 65C05: Monte Carlo methods 60G55: Point processes 60K15: Markov renewal processes, semi-Markov processes
Type
Research Article
Information
Journal of Applied Probability , Volume 44 , Issue 3 , September 2007 , pp. 806 - 823
Copyright
Copyright © Applied Probability Trust 2007 

Footnotes

∗

Current address: Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong. Email address: [email protected]

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