Large deviations principle by viscosity solutions: the case of diffusions with oblique Lipschitz reflections

Magdalena Kobylanski

Annales de l'I.H.P. Probabilités et statistiques (2013)

  • Volume: 49, Issue: 1, page 160-181
  • ISSN: 0246-0203

Abstract

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We establish a Large Deviations Principle for diffusions with Lipschitz continuous oblique reflections on regular domains. The rate functional is given as the value function of a control problem and is proved to be good. The proof is based on a viscosity solution approach. The idea consists in interpreting the probabilities as the solutions to some PDEs, make the logarithmic transform, pass to the limit, and then identify the action functional as the solution of the limiting equation.

How to cite

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Kobylanski, Magdalena. "Large deviations principle by viscosity solutions: the case of diffusions with oblique Lipschitz reflections." Annales de l'I.H.P. Probabilités et statistiques 49.1 (2013): 160-181. <http://eudml.org/doc/272029>.

@article{Kobylanski2013,
abstract = {We establish a Large Deviations Principle for diffusions with Lipschitz continuous oblique reflections on regular domains. The rate functional is given as the value function of a control problem and is proved to be good. The proof is based on a viscosity solution approach. The idea consists in interpreting the probabilities as the solutions to some PDEs, make the logarithmic transform, pass to the limit, and then identify the action functional as the solution of the limiting equation.},
author = {Kobylanski, Magdalena},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {large deviations principle; diffusions with oblique reflections; viscosity solutions; optimal control; optimal stopping; reflected diffusions; large deviations, small noise limit; Hamilton-Jacobi equations},
language = {eng},
number = {1},
pages = {160-181},
publisher = {Gauthier-Villars},
title = {Large deviations principle by viscosity solutions: the case of diffusions with oblique Lipschitz reflections},
url = {http://eudml.org/doc/272029},
volume = {49},
year = {2013},
}

TY - JOUR
AU - Kobylanski, Magdalena
TI - Large deviations principle by viscosity solutions: the case of diffusions with oblique Lipschitz reflections
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2013
PB - Gauthier-Villars
VL - 49
IS - 1
SP - 160
EP - 181
AB - We establish a Large Deviations Principle for diffusions with Lipschitz continuous oblique reflections on regular domains. The rate functional is given as the value function of a control problem and is proved to be good. The proof is based on a viscosity solution approach. The idea consists in interpreting the probabilities as the solutions to some PDEs, make the logarithmic transform, pass to the limit, and then identify the action functional as the solution of the limiting equation.
LA - eng
KW - large deviations principle; diffusions with oblique reflections; viscosity solutions; optimal control; optimal stopping; reflected diffusions; large deviations, small noise limit; Hamilton-Jacobi equations
UR - http://eudml.org/doc/272029
ER -

References

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