Related papers: Large Deviation Principle for McKean-Vlasov Quasil…

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…

As an important tool characterizing the long time behavior of Markov processes, the Donsker-Varadhan LDP (large deviation principle) does not directly apply to distribution dependent SDEs/SPDEs since the solutions are non-Markovian. We…

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.…

In this paper, we study the large deviation principle of invariant measures of stochastic reaction-diffusion lattice systems driven by multiplicative noise. We first show that any limit of a sequence of invariant measures of the stochastic…

The well-posedness is established for McKean-Vlasov SDEs driven by $\alpha$-stable noises ($1<\alpha<2$). In this model, the drift is H\"{o}lder continuous in space variable and Lipschitz continuous in distribution variable with respect to…

We study a class of reflected McKean-Vlasov diffusions over a convex domain with self-stabilizing coefficients. This includes coefficients that do not satisfy the classical Wasserstein Lipschitz condition. Further, the process is…

This paper is concerned with the large deviation principle of the non-local fractional stochastic reaction-diffusion equation with a polynomial drift of arbitrary degree driven by multiplicative noise defined on unbounded domains. We first…

In this paper, we establish large deviation principle for the strong solution of evolutionary p-Laplace equation driven by small multiplicative Brownian noise, where the weak convergence approach plays a key role. Moreover, by using…

We prove the the large deviation principle(LDP) for the law of the one-dimensional semilinear stochastic partial differential equations driven by nonlinear multiplicative noise. Firstly, combining the energy estimate and approximation…

We study the large deviations principle for locally periodic stochastic differential equations with small noise and fast oscillating coefficients. There are three possible regimes depending on how fast the intensity of the noise goes to…

In this paper, we present sufficient conditions and criteria to establish general large and moderate deviation principles for multivalued McKean-Vlasov stochastic differential equations (SDEs in short) by means of the weak convergence…

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 $D\subset {\mathbb R}^d$…

This work develops a particle system addressing the approximation of McKean-Vlasov stochastic differential equations (SDEs). The novelty of the approach lies in involving low discrepancy sequences nontrivially in the construction of a…

In this paper, a probabilistic interpretation for the viscosity solution of a parabolic partial differential equation is obtained by virtue of the solution of a class of quadratic backward stochastic differential equations (BSDEs, for…

In this paper, we consider stochastic reaction-diffusion equations with super-linear drift on the real line $\mathbb{R}$ driven by space-time white noise. A Freidlin-Wentzell large deviation principle is established by a modified weak…

This paper studies McKean-Vlasov stochastic differential equations (MVSDEs) whose drift coefficients grow super-linearly in both state variables and measure arguments, and whose diffusion coefficients exhibit super-linear growth in the…

In this paper, we establish the large deviation principles for stochastic porous media equations driven by time-dependent multiplicative noise on $\sigma$-finite measure space $(E,\mathcal{B}(E),\mu)$, and the Laplacian replaced by a…

In this paper, we investigate a class of McKean-Vlasov stochastic differential equations under L\'evy-type perturbations. We first establish the existence and uniqueness theorem for solutions of the McKean-Vlasov stochastic differential…

In this paper we study a large deviation principle of Freidlin-Wentzell type for pinned hypoelliptic diffusion measures associated with a natural sub-Laplacian on a compact sub-Riemannian manifold. To prove this large deviation principle,…

The Laplace principle for the strong solution of the stochastic shell model of turbulence perturbed by Levy noise is established in a suitable Polish space using weak convergence approach. The large deviation principle is proved using the…