Related papers: Large and moderate deviations principles and centr…

The asymptotic analysis of a class of stochastic partial differential equations (SPDEs) with fully locally monotone coefficients covering a large variety of physical systems, a wide class of quasilinear SPDEs and a good number of fluid…

We consider a sequence of processes defined on half-line for all non negative t. We give sufficient conditions for Large Deviation Principle (LDP) to hold in the space of continuous functions with a new metric that is more sensitive to…

Let $(a_k)_{k\in\mathbb N}$ be a sequence of integers satisfying the Hadamard gap condition $a_{k+1}/a_k>q>1$ for all $k\in\mathbb N$, and let $$ S_n(\omega) = \sum_{k=1}^n\cos(2\pi a_k \omega),\qquad n\in\mathbb N,\;\omega\in [0,1]. $$ The…

In this paper, we establish a large deviation principle for stochastic differential delay equations driven by both Brownian motions and Poisson random measures. The weak convergence method plays an important role.

The Moderate Deviations Principle (MDP) is well-understood for sums of independent random variables, worse understood for stationary random sequences, and scantily understood for random fields. Here it is established for splittable random…

In this paper we develop the large deviations principle and a rigorous mathematical framework for asymptotically efficient importance sampling schemes for general, fully dependent systems of stochastic differential equations of slow and…

In this paper we prove a large deviation principle (LDP) for the empirical measure of a general system of mean-field interacting diffusions with singular drift (as the number of particles tends to infinity) and show convergence to the…

In this paper, by using classical Faedo-Galerkin approximation and compactness method, the existence of martingale solutions for the stochastic 3D Navier-Stokes equations with nonlinear damping is obtained. The existence and uniqueness of…

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 work, we consider a wide two-layer neural network and study the behavior of its empirical weights under a dynamics set by a stochastic gradient descent along the quadratic loss with mini-batches and noise. Our goal is to prove a…

One says that the local large deviation principle (LLDP) is satisfied for a family of random vectors $\{\zeta_T\}_{T\ge 0}$ in $\mathbb R^d,$ $d\ge 1,$ if there exists a function $D:\mathbb R^d\to [0,\infty],$ $D\not \equiv \infty,$ such…

In this paper we study the moderate deviations principle (MDP) for slow-fast stochastic dynamical systems where the slow motion is governed by small fractional Brownian motion (fBm) with Hurst parameter $H\in(1/2,1)$. We derive conditions…

We study the large deviation behavior of a system of diffusing particles with a mean field interaction, described through a collection of stochastic differential equations, in which each particle is driven by a vanishing independent…

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 is concerned with the large deviation principle of the stochastic reaction-diffusion lattice systems defined on the N-dimensional integer set, where the nonlinear drift term is locally Lipschitz continuous with polynomial growth…

Let L be a positive line bundle over a projective complex manifold X. Consider the space of holomorphic sections of the tensor power of order p of L. The determinant of a basis of this space, together with some given probability measure on…

This paper is devoted to investigating the Freidlin-Wentzell's large deviation principle for a class of McKean-Vlasov quasilinear SPDEs perturbed by small multiplicative noise. We adopt the variational framework and the modified weak…

The main aim of this paper is to study the moderate deviation principle for McKean-Vlasov stochastic differential equations with multiple scales. Specifically, we are interested in the asymptotic estimates of the deviation processes…

For parabolic stochastic partial differential equations (SPDEs), we show that the numerical methods, including the spatial spectral Galerkin method and further the full discretization via the temporal accelerated exponential Euler method,…

We establish a central limit theorem and large deviations principle that characterises small noise fluctuations of the generalised Dean--Kawasaki stochastic PDE. The fluctuations agree to first order with fluctuations of certain interacting…