Abstract
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.
Highlights
Consider the following obstacle problems for quasilinear stochastic partial differential equations (SPDEs) in Rd : Applied Mathematics & Optimization (2021) 83:849–879dU (t, x) + 1 2 dU (t, x) + ∂i gi (t, x, U (t, x), ∇U (t, x))dt i =1+ f (t, x, U (t, x), ∇U (t, x))dt ∞+ h j (t, x, U (t, x), ∇U (t, x))d Btj = −R(dt, d x), (1.1) j =1U (t, x) ≥ L(t, x), (t, x) ∈ R+ × Rd,U (T, x) = (x), x ∈ Rd, (1.2)
Existence and uniqueness of the obstacle problems for quasi-linear SPDEs on the whole space Rd and driven by finite dimensional Brownian motions were studied in [20] using the approach of backward stochastic differential equations (BSDEs)
The advantage of the new sufficient condition is to shift the difficulty of proving the tightness of the perturbations of stochastic differential(partial differential) equations to a study of the continuity of deterministic skeleton equations associated with the stochastic equations
Summary
Consider the following obstacle problems for quasilinear stochastic partial differential equations (SPDEs) in Rd :. Existence and uniqueness of the obstacle problems for quasi-linear SPDEs on the whole space Rd and driven by finite dimensional Brownian motions were studied in [20] using the approach of backward stochastic differential equations (BSDEs). The advantage of the new sufficient condition is to shift the difficulty of proving the tightness of the perturbations of stochastic differential(partial differential) equations to a study of the continuity (with respect to the driving signals) of deterministic skeleton equations associated with the stochastic equations. This new sufficient condition is recently successfully applied to obtain a large deviation principle for stochastic conservation laws
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
