Related papers: Large Deviation Principle for Multi-Scale Fully Lo…
This paper is devoted to proving the strong averaging principle for slow-fast stochastic partial differential equations with locally monotone coefficients, where the slow component is a stochastic partial differential equations with locally…
Recently, extracting data-driven governing laws of dynamical systems through deep learning frameworks has gained a lot of attention in various fields. Moreover, a growing amount of research work tends to transfer deterministic dynamical…
We consider multiple time scales systems of stochastic differential equations with small noise in random environments. We prove a quenched large deviations principle with explicit characterization of the action functional. The random medium…
Stochastic gradient descent (SGD) has been widely used in machine learning due to its computational efficiency and favorable generalization properties. Recently, it has been empirically demonstrated that the gradient noise in several deep…
We prove the Large Deviation Principle for the empirical process in a system of locally interacting Brownian motions in the nonequilibrium dynamic. Such a phenomenon has been proven only for two lattice systems: the symmetric simple…
The paper concerns itself with establishing large deviation principles for a sequence of stochastic integrals and stochastic differential equations driven by general semimartingales in infinite-dimensional settings. The class of…
In this paper, we establish a large deviation principle for the stochastic generalized Ginzburg-Landau equation driven by jump noise. The main difficulties come from the highly non-linear coefficient. Here we adopt a new sufficient…
In this paper, we consider a class of reflected stochastic differential equations for which the constraint is not on the paths of the solution but on its law. We establish a small noise large deviation principle, a large deviation for short…
In this paper, a large deviation principle for the strong solution of the p-Laplace equation on unbounded domain driven by small multiplicative Brownian noise is established. The weak convergence approach and the localized time increment…
The goal of the paper is to analytically examine escape probabilities for dynamical systems driven by symmetric $\alpha$-stable L\'evy motions. Since escape probabilities are solutions of a type of integro-differential equations (i.e.,…
Semilinear stochastic evolution equations with multiplicative Poisson noise and monotone nonlinear drift are considered. We do not impose coercivity conditions on coefficients. A novel method of proof for establishing existence and…
In this paper, we establish a central limit theorem and a moderate deviations for 2D stochastic primitive equations with multiplicative noise. The proof is mainly based on the weak convergence approach.
We establish a large deviation principle for the occupation measure of the stochastic real Ginzburg-Landau equation driven by $\alpha$-stable noises. The proof is based on a hyper-exponential recurrence criterion. Our result indicates a…
We study a large deviation principle for a system of stochastic reaction--diffusion equations (SRDEs) with a separation of fast and slow components and small noise in the slow component. The derivation of the large deviation principle is…
This paper develops and analyzes an optimal-order semi-discrete scheme and its fully discrete finite element approximation for nonlinear stochastic elastic wave equations with multiplicative noise. A non-standard time-stepping scheme is…
We investigate the stabilization of unstable multidimensional partially observed single-sensor and multi-sensor linear systems driven by unbounded noise and controlled over discrete noiseless channels under fixed-rate information…
The one-dimensional SDE with non Lipschitz diffusion coefficient $dX_{t} = b(X_{t})dt + \sigma X_{t}^{\gamma} dB_{t}, \ X_{0}=x, \ \gamma<1$ is widely studied in mathematical finance. Several works have proposed asymptotic analysis of…
In this paper, we first provide a criterion on uniform large deviation principles (ULDP) of stochastic differential equations under Lyapunov conditions on the coefficients, which can be applied to stochastic systems with coefficients of…
In this paper, we establish a large deviation principle for a stochastic evolution equation which describes the system governing the nematic liquid crystals driven by pure jump noise. The proof is based on the weak convergence approach.
We propose and analyse a novel, fully discrete numerical algorithm for the approximation of the generalised Stokes system forced by transport noise -- a prototype model for non-Newtonian fluids including turbulence. Utilising the Gradient…