Related papers: Large Deviations of continuous Gaussian processes:…
We consider a two-dimensional Hamiltonian system perturbed by a small diffusion term, whose coefficient is state-dependent and non-degenerate. As a result, the process consists of the fast motion along the level curves and slow motion…
We introduce a numerical procedure to evaluate directly the probabilities of large deviations of physical quantities, such as current or density, that are local in time. The large-deviation functions are given in terms of the typical…
We consider the one-dimensional stochastic heat and wave equations driven by Gaussian noises with constant initial conditions. We study the spatial average of the solutions on an interval of length $R$ and show that the family of laws of…
Localized sufficient conditions for the large deviation principle of the given stochastic differential equations will be presented for stochastic differential equations with non-Lipschitzian and time-inhomogeneous coefficients, which is…
This paper presents a general approach to linear stochastic processes driven by various random noises. Mathematically, such processes are described by linear stochastic differential equations of arbitrary order (the simplest non-trivial…
Stochastic processes with random reinforced relocations have been introduced in the physics literature to model animal foraging behaviour. Such a process evolves as a Markov process, except at random relocation times, when it chooses a time…
In this paper we prove scalar and sample path large deviation principles for a large class of Poisson cluster processes. As a consequence, we provide a large deviation principle for ergodic Hawkes point processes.
In this short note we consider semi-Markov processes satisfying the condition of direction-time independence (Markov renewal processes). We derive large deviation principles and fluctuation theorems for the empirical current and the…
Birth-death processes form a natural class where ideas and results on large deviations can be tested. In this paper, we derive a large deviation principle under the assumption that the rate of a jump down (death) is growing asymptotically…
A large deviation function mathematically characterizes the statistical property of atypical events. Recently, in non-equilibrium statistical mechanics, large deviation functions have been used to describe universal laws such as the…
Let $X$ be a L\'evy process with regularly varying L\'evy measure $\nu$. We obtain sample-path large deviations for scaled processes $\bar X_n(t) \triangleq X(nt)/n$ and obtain a similar result for random walks. Our results yield detailed…
In this work, we study large deviation properties of the covariance process in fully connected Gaussian deep neural networks. More precisely, we establish a large deviation principle (LDP) for the covariance process in a functional…
A new approach for the analysis of Langevin-type stochastic processes in the presence of strong measurement noise is presented. For the case of Gaussian distributed, exponentially correlated, measurement noise it is possible to extract the…
In this paper, we present a large-deviation theory developed for functionals of canonical Gibbs processes, i.e., Gibbs processes with respect to the binomial point process. We study the regime of a fixed intensity in a sequence of…
This paper focuses on systems of nonlinear second-order stochastic differential equations with multi-scales. The motivation for our study stems from mathematical physics and statistical mechanics, for examples, Langevin dynamics and…
Gaussian processes with derivative information are useful in many settings where derivative information is available, including numerous Bayesian optimization and regression tasks that arise in the natural sciences. Incorporating derivative…
We study the large deviations principle for locally periodic stochastic differential equations with small noise and fast oscillating coefficients. There are three possible regimes depending on how fast the intensity of the noise goes to…
Large-scale Gaussian process inference has long faced practical challenges due to time and space complexity that is superlinear in dataset size. While sparse variational Gaussian process models are capable of learning from large-scale data,…
An extension and generalization of a recently presented approach for the analysis of Langevin-type stochastic processes in the presence of strong measurement noise is presented. For a stochastic process in N dimensions which is superimposed…
A large deviation principle is established for a two-scale stochastic system in which the slow component is a continuous process given by a small noise finite dimensional It\^{o} stochastic differential equation, and the fast component is a…