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Local Linear Approximations of Jump Diffusion Processes

Part of: Markov processes Stochastic analysis

Published online by Cambridge University Press:  14 July 2016

J. C. Jimenez  and
F. Carbonell
J. C. Jimenez*
Affiliation:
Instituto de Cibernética, Matemática y Física
F. Carbonell*
Affiliation:
Instituto de Cibernética, Matemática y Física
*
∗ Postal address: Departamento de Sistemas Adaptativos, Instituto de Cibernética, Matemática y Física, Calle 15, No. 551, Vedado, La Habana 4, C.P. 10400, Cuba.
∗ Postal address: Departamento de Sistemas Adaptativos, Instituto de Cibernética, Matemática y Física, Calle 15, No. 551, Vedado, La Habana 4, C.P. 10400, Cuba.
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Abstract

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Local linear approximations have been the main component in the construction of a class of effective numerical integrators and inference methods for diffusion processes. In this note, two local linear approximations of jump diffusion processes are introduced as a generalization of the usual ones. Their rate of uniform strong convergence is also studied.

Keywords

Jump diffusion processstochastic differential equationnumerical integrationlocal linearization methodpseudo-likelihood method

MSC classification

Primary: 60J75: Jump processes 60J60: Diffusion processes 60H35: Computational methods for stochastic equations
Type
Research Papers
Information
Journal of Applied Probability , Volume 43 , Issue 1 , March 2006 , pp. 185 - 194
Copyright
© Applied Probability Trust 2006 

Footnotes

Partially supported by the research grant 03-059 RG/MATHS/LA from the ThirdWorld Academy of Science.

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