Related papers: Large Deviation Minimisers for Stochastic Partial …
We prove the small-noise large deviation principle for the three-dimensional primitive equations with transport noise and turbulent pressure. Transport noise is important for geophysical fluid dynamics applications, as it takes into account…
The Freidlin-Wentzell large deviation principle is established for the distributions of stochastic evolution equations with general monotone drift and small multiplicative noise. As examples, the main results are applied to derive the large…
The aim of this paper is to develop tractable large deviation approximations for the empirical measure of a small noise diffusion. The starting point is the Freidlin-Wentzell theory, which shows how to approximate via a large deviation…
We consider the rates of noise-induced switching between the stable states of dissipative dynamical systems with delay and also the rates of noise-induced extinction, where such systems model population dynamics. We study a class of systems…
Small random perturbations may have a dramatic impact on the long time evolution of dynamical systems, and large deviation theory is often the right theoretical framework to understand these effects. At the core of the theory lies 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.
Distribution-dependent stochastic dynamical systems arise widely in engineering and science. We consider a class of such systems which model the limit behaviors of interacting particles moving in a vector field with random fluctuations. We…
Stochastic systems are used to model a variety of phenomena in which noise plays an essential role. In these models, one potential goal is to determine if noise can induce transitions between states, and if so, to calculate the most…
This paper is concerned with a dissipativity theory for dynamical systems governed by linear Ito stochastic differential equations driven by random noise with an uncertain drift. The deviation of the noise from a standard Wiener process in…
This paper presents a heuristic derivation of a geometric minimum action method that can be used to determine most-probable transition paths in noise-driven dynamical systems. Particular attention is focused on systems that violate detailed…
We often rely on probabilistic measures -- e.g. event probability or expected time -- to characterize systems' safety. However, determining these quantities for extremely low-probability events is generally challenging, as standard safety…
In this paper, we study the problem of how to optimally steer the state covariance of a general continuous-time linear stochastic system over a finite time interval subject to additive noise. Optimality here means reaching a target state…
Noise-induced transitions between metastable fixed points in systems evolving on multiple time scales are analyzed in situations where the time scale separation gives rise to a slow manifold with bifurcation. This analysis is performed…
Large deviation results are given for a class of perturbed nonhomogeneous Markov chains on finite state space which formally includes some stochastic optimization algorithms. Specifically, let {P_n} be a sequence of transition matrices on a…
We study the large deviation principle (LDP) for locally damped nonlinear wave equations perturbed by a bounded noise. When the noise is sufficiently non-degenerate, we establish the LDP for empirical distributions with lower bound of a…
We study a large deviation functional of density fluctuation by analyzing stochastic non-linear diffusion equations driven by the difference between the densities fixed at the boundaries. By using a fundamental equality that yields the…
In this paper, we present large deviation theory that characterizes the exponential estimate for rare events of stochastic dynamical systems in the limit of weak noise. We aim to consider next-to-leading-order approximation for more…
We focus in this paper on the stochastic stabilization problems of PDEs by Levy noise. Sufficient conditions under which the perturbed systems decay exponentially with a general rate function are provided and some examples are constructed…
In this paper, we introduce a mathematical apparatus that is relevant for understanding a dynamical system with small random perturbations and coupled with the so-called transmutation process -- where the latter jumps from one mode to…
The large deviation principle is established for the distributions of a class of generalized stochastic porous media equations for both small noise and short time.