Variational representations for continuous time processes

A variational formula for positive functionals of a Poisson random measure and Brownian motion is proved. The formula is based on the relative entropy representation for exponential integrals, and can be used to prove large deviation type estimates. A general large deviation result is proved, and il...

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Bibliographic Details
Published inAnnales de l'I.H.P. Probabilités et statistiques Vol. 47; no. 3; pp. 725 - 747
Main Authors BUDHIRAJA, Amarjit, DUPUIS, Paul, MAROULAS, Vasileios
Format Journal Article
LanguageEnglish
Published Paris Elsevier 01.08.2011
Institut Henri Poincaré
Subjects
60F10
60G51
60H15
Exact sciences and technology
General topics
Infinite-dimensional Brownian motion
Jump-diffusions
Large deviations
Limit theorems
Mathematics
Poisson random measure
Probability and statistics
Probability theory and stochastic processes
Sciences and techniques of general use
Statistics
Stochastic processes
Variational representations
Probability theory
Random measure
Continuous time
Large deviations
Jump-diffusions
Poisson random measure
Large deviation
Functional
Random motion
Brownian motion
Relative entropy
secondary 60G51
Jump diffusion
Variational representations
Infinite-dimensional Brownian motion
Primary 60F10
Integral representation
60H15
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Summary:A variational formula for positive functionals of a Poisson random measure and Brownian motion is proved. The formula is based on the relative entropy representation for exponential integrals, and can be used to prove large deviation type estimates. A general large deviation result is proved, and illustrated with an example.
ISSN:0246-0203
DOI:10.1214/10-AIHP382