Related papers: Reductions and deviations for stochastic partial d…

In this paper, we proved moderate deviation principles for a fully coupled two-time-scale stochastic systems, where the slow process is given by stochastic differential equations with small noise, while the fast process is a rapidly…

Neural Stochastic Differential Equations model a dynamical environment with neural nets assigned to their drift and diffusion terms. The high expressive power of their nonlinearity comes at the expense of instability in the identification…

Mathematical models for complex systems are often accompanied with uncertainties. The goal of this paper is to extract a stochastic differential equation governing model with observation on stationary probability distributions. We develop a…

Additive noise in Partial Differential equations, in particular those of fluid mechanics, has relatively natural motivations. The aim of this work is showing that suitable multiscale arguments lead rigorously, from a model of fluid with…

A change of variables is introduced to reduce certain nonlinear stochastic evolution equations with multiplicative noise to the corresponding deterministic equation. The result is then used to investigate a stochastic porous medium…

Stochastic differential equations (SDEs) are a ubiquitous modeling framework that finds applications in physics, biology, engineering, social science, and finance. Due to the availability of large-scale data sets, there is growing interest…

In this paper we investigate the well-posedness of backward or forward stochastic differential equations whose law is constrained to live in an a priori given (smooth enough) set and which is reflected along the corresponding ''normal''…

Increasingly larger data sets of processes in space and time ask for statistical models and methods that can cope with such data. We show that the solution of a stochastic advection-diffusion partial differential equation provides a…

Theoretical studies have shown that stochasticity can affect the dynamics of ecosystems in counter-intuitive ways. However, without knowing the equations governing the dynamics of populations or ecosystems, it is difficult to ascertain the…

The technique of stochastic solutions, previously used for deterministic equations, is here proposed as a solution method for partial differential equations driven by distribution-valued noises.

This work is concerned with a singularly perturbed stochastic nonlinear wave equation with a random dynamical boundary condition. A splitting skill is used to derive the approximating equation of the system in the sense of probability…

In this article, we study the dynamics of a nonlinear system governed by an ordinary differential equation under the combined influence of fast periodic sampling with period $\delta$ and small jump noise of size $\varepsilon, 0<…

Dynamical systems theory provides powerful methods to extract effective macroscopic dynamics from complex systems with slow modes and fast modes. Here we derive and theoretically support a macroscopic, spatially discrete, model for a class…

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…

Random invariant manifolds are geometric objects useful for understanding complex dynamics under stochastic influences. Under a nonuniform hyperbolicity or a nonuniform exponential dichotomy condition, the existence of random pseudo-stable…

Noisy dynamical models are employed to describe a wide range of phenomena. Since exact modeling of these phenomena requires access to their microscopic dynamics, whose time scales are typically much shorter than the observable time scales,…

We study classical stochastic systems with discrete states, coupled to switching external environments. For fast environmental processes we derive reduced dynamics for the system itself, focusing on corrections to the adiabatic limit of…

Dynamical system models with delayed dynamics and small noise arise in a variety of applications in science and engineering. In many applications, stable equilibrium or periodic behavior is critical to a well functioning system. Sufficient…

Stochastic partial differential equations driven by Poisson random measures (PRM) have been proposed as models for many different physical systems, where they are viewed as a refinement of a corresponding noiseless partial differential…

We investigate the approximate dynamics of several differential equations when the solutions are restricted to a sparse subset of a given basis. The restriction is enforced at every time step by simply applying soft thresholding to the…