Related papers: Large deviation principle for certain spatially li…

The convergence of the first order Euler scheme and an approximative variant thereof, along with convergence rates, are established for rough differential equations driven by c\`adl\`ag paths satisfying a suitable criterion, namely the…

We investigate large deviations for a family of conservative stochastic PDEs (conservation laws) in the asymptotic of jointly vanishing noise and viscosity. We obtain a first large deviations principle in a space of Young measures. The…

We consider a non-stationary Cox-Ingersoll-Ross process. We establish a sharp large deviation principle for the maximum likelihood estimator of its drift parameter.

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…

Using the hyper-exponential recurrence criterion, a large deviation principle for the occupation measure is derived for a class of non-linear monotone stochastic partial differential equations. The main results are applied to many concrete…

The Airy point process is a determinantal point process that arises from the spectral edge of the Gaussian Unitary Ensemble. In this paper, we establish a large deviation principle for the Airy point process. Our result also extends to…

In the framework of Harnack type Dirichlet forms, we prove a large deviation principle for the asymptotics of reversible Markov processes with rate function given by the energy of the paths.

In this paper we consider the Allen-Cahn equation perturbed by a stochastic flux term and prove a large deviation principle. Using an associated stochastic flow of diffeomorphisms the equation can be transformed to a parabolic partial…

The main goal of this article is to study the effect of small, highly nonlinear, unbounded drifts (small time large deviation principle (LDP) based on exponential equivalence arguments) for a class of stochastic partial differential…

We develop a pathwise theory for scalar conservation laws with quasilinear multiplicative rough path dependence, a special case being stochastic conservation laws with quasilinear stochastic dependence. We introduce the notion of pathwise…

For Gaussian random fields with values in $\mathbb{R}^d$, sharp upper and lower bounds on the probability of hitting a fixed set have been available for many years. These apply in particular to the solutions of systems of linear SPDEs. For…

We study linear rough partial differential equations in the setting of [Friz and Hairer, Springer, 2014, Chapter 12]. More precisely, we consider a linear parabolic partial differential equation driven by a deterministic rough path…

Recent works have shown that high probability metrics with stochastic gradient descent (SGD) exhibit informativeness and in some cases advantage over the commonly adopted mean-square error-based ones. In this work we provide a formal…

We prove a large deviations principle for the probabilistic Schwarzian Field Theory at low temperatures. We demonstrate that the good rate function is equal to the action of the Schwarzian Field Theory, and we find its minimisers. In…

In this paper we study rough differential equations driven by Gaussian rough paths from the viewpoint of Malliavin calculus. Under mild assumptions on coefficient vector fields and underlying Gaussian processes, we prove that solutions at a…

We consider anticipative Stratonovich stochastic differential equations driven by some stochastic process (not necessarily a semi-martingale). No adaptedness of initial point or vector fields is assumed. Under a simple condition on the…

For a class of additive processes driven by the affine recursion $X_{n+1} = A_n X_n + B_n$, we develop a sample-path large deviations principle in the $M_1'$ topology on $D [0,1]$. We allow $B_n$ to have both signs and focus on the case…

We propose a surface hopping Gaussian beam method to numerically solve a class of high frequency linear transport systems in high spatial dimensions, based on asymptotic analysis. The stochastic surface hopping is combined with Gaussian…

We establish the existence and uniqueness of strong solutions, in both the PDE and probabilistic sense, for a broad class of nonlinear stochastic partial differential equations (SPDEs) on a bounded domain $\mathscr{O}\subset \mathbb{R}^d$…

The large deviations principles are established for a class of multidimensional degenerate stochastic differential equations with reflecting boundary conditions. The results include two cases where the initial conditions are adapted and…