Related papers: Large Deviations Principles for Langevin Equations…
Large deviations principle is obtained for terminating multidimensional compound renewal processes. We also obtained the asymptotic of large deviations for the case when a Gibbs change of the original probability measure takes place. The…
Boltzmann-Sanov and Cramer-Chernoff's theorems provide large deviation probabilities, entropy, and rate functions for the spatial distribution of systems and the total internal energy of an ensemble respectively. By the method of Lagrange's…
Moderate deviation principles for empirical measure processes associated with weakly interacting Markov processes are established. Two families of models are considered: the first corresponds to a system of interacting diffusions whereas…
We establish a Large Deviations Principle for stochastic processes with Lipschitz continuous oblique reflections on regular domains. The rate functional is given as the value function of a control problem and is proved to be good. The proof…
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…
We propose a computational method for large deviation statistics of time-averaged quantities in general Markov processes. In our proposed method, we repeat a response measurement against external forces, where the forces are determined by…
We take the point of view of a particle performing random walk with bounded jumps on $\mathbb{Z}^d$ in a stationary and ergodic random environment. We prove the quenched large deviation principle (LDP) for the pair empirical measure of the…
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…
One of the main contributions of this paper is to illustrate how large deviation theory can be used to determine the equilibrium distribution of a basic droplet model that underlies a number of important models in material science and…
In this paper, we consider Langevin processes with mechanical constraints. The latter are a fundamental tool in molecular dynamics simulation for sampling purposes and for the computation of free energy differences. The results of this…
We prove the small-noise large deviation principle (LDP) for stochastic evolution equations in an $L^2$-setting. As the coefficients are allowed to be non-coercive, our framework encompasses a much broader scope than variational settings.…
We derive an annealed large deviation principle (LDP) for the normalised and rescaled local times of a continuous-time random walk among random conductances (RWRC) in a time-dependent, growing box in $\Z^d$. We work in the interesting case…
This paper is devoted to the development of a theoretical and computational framework to efficiently sample the statistically significant thermally activated reaction pathways, in multi-dimensional systems obeying Langevin dynamics. We show…
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 goal of this paper is to study the Moderate Deviation Principle (MDP) for a system of stochastic reaction-diffusion equations with a time-scale separation in slow and fast components and small noise in the slow component. Based on weak…
We derive a large deviation principle for families of random variables in the basin of attraction of spectrally positive stable distributions by proving a uniform version of the Tauberian theorem for Laplace-Stieltjes transforms. The main…
The Boltzmann equation is one of the most famous equations and has vast applications in modern science. In the current study, we take the randomness of binary collisions into consideration and generalize the classical Boltzmann equation…
We establish a strong law of large numbers for one-dimensional continuous-time random walks in dynamic random environments under two main assumptions: the environment is required to satisfy a decoupling inequality that can be interpreted as…
We study rare events in systems of diffusive fields driven out of equilibrium by the boundaries. We present a numerical technique and use it to calculate the probabilities of rare events in one and two dimensions. Using this technique, we…
Large deviation theory (LDT) provides a mathematical framework to quantify the probabilities of rare events in stochastic systems. In this study, we applied LDT to model a chemical reaction system and demonstrated that the fluctuation…