Related papers: Large deviation principle for a stochastic nonline…

We study large deviations from the invariant measure for nonlinear Schr\"odinger equations with colored noises on determining modes. The proof is based on a new abstract criterion, inspired by [V. Jak\v{s}i\'{c} et al., Comm. Pure Appl.…

We consider the damped nonlinear wave (NLW) equation driven by a spatially regular white noise. Assuming that the noise is non-degenerate in all Fourier modes, we establish a large deviations principle (LDP) for the occupation measures of…

In this paper, we consider the large deviations for dynamical Schr\"odinger problems, using the variational approach developed by Dupuis, Ellis, Budhiraja, and others. Recent results on scaled families of Schr\"odinger problems, in…

In this paper, we consider the large deviations principles (LDPs) for the stochastic linear Schr\"odinger equation and its symplectic discretizations. These numerical discretizations are the spatial semi-discretization based on spectral…

A Freidlin-Wentzell type large deviation principle is established for stochastic partial differential equations with slow and fast time-scales, where the slow component is a one-dimensional stochastic Burgers equation with small noise and…

We consider a stochastic partial differential equation with logarithmic (or negative power) nonlinearity, with one reflection at 0 and with a constraint of conservation of the space average. The equation, driven by the derivative in space…

We demonstrate the large deviation property for the mild solutions of stochastic evolution equations with monotone nonlinearity and multiplica- tive noise. This is achieved using the recently developed weak convergence method, in studying…

Localized sufficient conditions for the large deviation principle of the given stochastic differential equations will be presented for stochastic differential equations with non-Lipschitzian and time-inhomogeneous coefficients, which is…

We deal with a class of abstract nonlinear stochastic models, which covers many 2D hydrodynamical models including 2D Navier-Stokes equations, 2D MHD models and 2D magnetic B\'enard problem and also some shell models of turbulence. We first…

We study the cubic weakly nonlinear Schr\"odinger equation with randomized spatially quasi-periodic initial data in higher dimensions. Under a polynomial decay assumption in Fourier space, we establish a {\em Large Deviations Principle} for…

We investigate and solve the weak noise theory for the semi-discrete O'Connell-Yor directed polymer. In the large deviation regime, the most probable evolution of the partition function obeys a classical non-linear system which is a…

We study the validity of a large deviation principle for a class of stochastic nonlinear damped wave equations, of Klein-Gordon type, in the joint small mass and small noise limit. The friction term is assumed to be state dependent.

We prove the small-noise large deviation principle (LDP) for stochastic evolution equations in an $L^2$-setting. As the coefficients are allowed to be non-coercive, our framework encompasses a much broader scope than variational settings.…

We study the large deviations of a simple noise-perturbed dynamical system having continuous sets of steady states, which mimick those found in some partial differential equations related, for example, to turbulence problems. The system is…

We consider the Cauchy problem of a system of quadratic derivative nonlinear Schr\"odinger equations which was introduced by M. Colin and T. Colin (2004) as a model of laser-plasma interaction. For the nonperiodic case, the author proved…

We prove a large deviation principle result for solutions of abstract stochastic evolution equations perturbed by small Levy noise. We use general large deviations theorems of Varadhan and Bryc, viscosity solutions of integro-partial…

In this work, we investigate the McKean-Vlasov stochastic partial differential equations driven by Poisson random measure. By adapting the variational framework, we prove the well-posedness and large deviation principle for a class of…

In this paper, we propose and analyze an adaptive time-stepping fully discrete scheme which possesses the optimal strong convergence order for the stochastic nonlinear Schr\"odinger equation with multiplicative noise. Based on the splitting…

We prove a Freidlin-Wentzell large deviation principle for general stochastic evolution equations with small perturbation multiplicative noises. In particular, our general result can be used to deal with a large class of quasi linear…

We prove the large deviation principle for the law of the solutions to a class of parabolic semilinear stochastic partial differential equations driven by multiplicative noise, in $C\big([0,T]:L^\rho(D)\big)$, where $D\subset {\mathbb R}^d$…