Related papers: Large Deviation Minimisers for Stochastic Partial …
We consider statistics for stochastic evolution equations in Hilbert space with emphasis on stochastic partial differential equations (SPDEs). We observe a solution process under additional measurement errors and want to estimate a real or…
Multiplicative noise models are often used instead of additive noise models in cases in which the noise variance depends on the state. Furthermore, when Poisson distributions with relatively small counts are approximated with normal…
Given a discrete stochastic process, for example a chemical reaction system or a birth and death process, we often want to find a continuous stochastic approximation so that the techniques of stochastic differential equations may be brought…
We prove a maximal-type large deviation principle for dynamical systems with arbitrarily slow polynomial mixing rates. Also several applications, particularly to billiard systems, are presented.
This paper studies the distributed optimization problem under the influence of heavy-tailed gradient noises. Here, a heavy-tailed noise means that the noise does not necessarily satisfy the bounded variance assumption. Instead, it satisfies…
In this paper, we establish a large deviation principle for 2D stochastic Chemotaxis-Navier-Stokes equation perturbed by a small multiplicative noise. The main difficulties come from the lack of a suitable compact embedding into the space…
Stochastic Gradient Descent (SGD) is the workhorse algorithm of deep learning technology. At each step of the training phase, a mini batch of samples is drawn from the training dataset and the weights of the neural network are adjusted…
A diffusive system coupled to unequal boundary reservoirs reaches a non-equilibrium steady state. While the full-counting-statistics of current fluctuations in these states are well understood for generic systems, results for steady-state…
This work is devoted to the investigation of the most probable transition time between metastable states for stochastic dynamical systems. Such a system is modeled by a stochastic differential equation with non-vanishing Brownian noise, and…
The aim of the present paper is to provide necessary and sufficient conditions to maintain a stochastic coupled system, with porous media components and gradient-type noise in a prescribed set of constraints by using internal controls. This…
Consider a collection of particles whose state evolution is described through a system of interacting diffusions in which each particle is driven by an independent individual source of noise and also by a small amount of noise that is…
We consider the problem of signal estimation (denoising) from a statistical mechanical perspective, using a relationship between the minimum mean square error (MMSE), of estimating a signal, and the mutual information between this signal…
In this paper, we establish large deviation principle for the strong solution of a doubly nonlinear PDE driven by small multiplicative Brownian noise. Motononicity arguments and the weak convergence approach have been exploited in the…
There is a reasonable possibility that the present-day Atlantic Meridional Overturning Circulation is in a bi-stable regime and hence it is relevant to compute probabilities and pathways of noise-induced transitions between the stable…
Optimal control theory deals with finding protocols to steer a system between assigned initial and final states, such that a trajectory-dependent cost function is minimized. The application of optimal control to stochastic systems is an…
We prove a large deviation principle for stochastic differential equations driven by semimartingales, with additive controls. Conditions are given in terms of characteristics of driven semimartingales, so that if the noise-control pairs…
We develop a provably efficient importance sampling scheme that estimates exit probabilities of solutions to small-noise stochastic reaction-diffusion equations from scaled neighborhoods of a stable equilibrium. The moderate deviation…
In existing distributed stochastic optimization studies, it is usually assumed that the gradient noise has a bounded variance. However, recent research shows that the heavy-tailed noise, which allows an unbounded variance, is closer to…
A numerical model based on the finite-difference time-domain method is developed to simulate fluctuations which accompany the dephasing of atomic polarization and the decay of excited state's population. This model is based on the…
Denoising has always been theoretically considered as removal of high frequency disturbances having Gaussian distribution. Here we relax this assumption and the method used here is completely different from traditional thresholding schemes.…