Related papers: Large deviations for nematic liquid crystals drive…
In this paper, we study the asymptotic behavior of randomly perturbed path-dependent stochastic differential equations with small parameter $\vartheta_{\varepsilon}$, when $\varepsilon \rightarrow 0$, $\vartheta_\varepsilon$ goes to $0$.…
We study nonlinear wave equations perturbed by transport noise acting either on the displacement or on the velocity. Such noise models random advection and, under suitable scaling of space covariance, may generate an effective dissipative…
This paper considers stochastic population dynamics driven by Levy noise. The contributions of this paper lie in that (a) Using Khasminskii-Mao theorem, we show that the stochastic differential equation associated with the model has a…
In this paper, the optimal control for discrete-time systems driven by fractional noises is studied. A stochastic maximum principle is obtained by introducing a backward stochastic difference equation contains both fractional noises and the…
Stochastic systems characterised by a random driving in a form of the general stable noise are considered. The particle experiences long rests due to the traps the density of which is position-dependent and obeys a power-law form attributed…
The big jump principle explains the emergence of extreme events for physical quantities modelled by a sum of independent and identically distributed random variables which are heavy-tailed. Extreme events are large values of the sum and…
For one-dimensional Jump-Drift and Jump-Diffusion processes converging towards some steady state, the large deviations of a long dynamical trajectory are described from two perspectives. Firstly, the joint probability of the empirical…
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 we consider non convex control problems of stochastic differential equations driven by relaxed controls. We present existence of optimal controls and then develop necessary conditions of optimality. We cover both continuous…
The large deviation properties of equilibrium (reversible) lattice gases are mathematically reasonably well understood. Much less is known in non--equilibrium, namely for non reversible systems. In this paper we consider a simple example of…
We address a class of backward stochastic differential equations on a bounded interval, where the driving noise is a marked, or multivariate, point process. Assuming that the jump times are totally inaccessible and a technical condition…
A variational lattice model is proposed to define an evolution of sets from a single point (nucleation) following a criterion of "maximization" of the perimeter. At a discrete level, the evolution has a "checkerboard" structure and its…
In this article, we establish the Freidlin-Wentzell type large deviation principle and central limit theorem for stochastic fractional conservation laws with small multiplicative noise in kinetic formulation framework. The weak convergence…
We study the stochastic motion of a droplet in a stochastic Cahn-Hilliard equation in the sharp interface limit for sufficiently small noise. The key ingredient in the proof is a deterministic slow manifold, where we show its stability for…
In the present paper we study a stochastic evolution equation for shell (SABRA \& GOY) models with pure jump \levy noise $L=\sum_{k=1}^\infty l_k(t)e_k$ on a Hilbert space $\h$. Here $\{l_k, k\in \mathbb{N}\}$ is a family of independent and…
How condensed-matter simulations depend on the number of molecules being simulated ($N$) is sometimes itself a valuable piece of information. Liquid crystals provide a case in point. Light scattering and $2d$-IR experiments on…
Additive noise in Partial Differential equations, in particular those of fluid mechanics, has relatively natural motivations. The aim of this work is showing that suitable multiscale arguments lead rigorously, from a model of fluid with…
We analyze the dynamical evolution of systems which obey simple growth laws, like diffusion limited aggregation or dielectric breakdown. We show that, if the developing patterns is sufficiently complex, a scale invariant noise spectrum is…
In this article, we consider slow-fast McKean-Vlasov stochastic differential equations driven by Brownian motions and fractional Brownian motions. We give a definition of the large deviation principle (LDP) on the product space related to…
We prove the large deviation principle for the trajectory of a broad class of mean field interacting Markov jump processes via a general analytic approach based on viscosity solutions. Examples include generalized Ehrenfest models as well…