Variational representations for continuous time processes
Annales de l'I.H.P. Probabilités et statistiques, Volume 47 (2011) no. 3, p. 725-747

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.

Une formule variationnelle pour des fonctionnelles positives d'une mesure de Poisson aléatoire et d'un mouvement brownien est démontrée. Cette formule provient de la représentation des intégrales exponentielles par l'entropie relative, et peut être utilisée pour obtenir des estimées de grandes déviations. Un résultat de grandes déviations général est démontré.

DOI : https://doi.org/10.1214/10-AIHP382
Classification:  60F10,  60G51,  60H15
Keywords: variational representations, Poisson random measure, infinite-dimensional brownian motion, large deviations, jump-diffusions
@article{AIHPB_2011__47_3_725_0,
     author = {Budhiraja, Amarjit and Dupuis, Paul and Maroulas, Vasileios},
     title = {Variational representations for continuous time processes},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Gauthier-Villars},
     volume = {47},
     number = {3},
     year = {2011},
     pages = {725-747},
     doi = {10.1214/10-AIHP382},
     zbl = {1231.60018},
     mrnumber = {2841073},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_2011__47_3_725_0}
}
Budhiraja, Amarjit; Dupuis, Paul; Maroulas, Vasileios. Variational representations for continuous time processes. Annales de l'I.H.P. Probabilités et statistiques, Volume 47 (2011) no. 3, pp. 725-747. doi : 10.1214/10-AIHP382. http://www.numdam.org/item/AIHPB_2011__47_3_725_0/

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