Large Deviation Principles of Obstacle Problems for Quasilinear Stochastic PDEs

In this paper, we first present a sufficient condition(a variant) for the large deviation criteria of Budhiraja, Dupuis and Maroulas for functionals of Brownian motions. The sufficient condition is particularly more suitable for stochastic differential/partial differential equations with reflection....

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Bibliographic Details
Published in:Applied mathematics & optimization 2021-04, Vol.83 (2), p.849-879
Main Authors: Matoussi, Anis, Sabbagh, Wissal, Zhang, Tusheng
Format: Article
Language:English
Subjects:
Barriers
Calculus of Variations and Optimal Control
Optimization
Control
Deviation
Mathematical analysis
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Numerical and Computational Physics
Partial differential equations
Simulation
Systems Theory
Theoretical
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Summary:In this paper, we first present a sufficient condition(a variant) for the large deviation criteria of Budhiraja, Dupuis and Maroulas for functionals of Brownian motions. The sufficient condition is particularly more suitable for stochastic differential/partial differential equations with reflection. We then apply the sufficient condition to establish a large deviation principle for obstacle problems of quasi-linear stochastic partial differential equations. It turns out that the backward stochastic differential equations will also play an important role.
ISSN:0095-4616
1432-0606
DOI:10.1007/s00245-019-09570-5