Related papers: Stochastic differential equations driven by loops

In this article we study the existence and uniqueness of solutions of stochastic continuity equation with irregular coefficients.

Random invariant manifolds often provide geometric structures for understanding stochastic dynamics. In this paper, a dynamical approximation estimate is derived for a class of stochastic partial differential equations, by showing that the…

In this paper, we introduce the idea of stochastic integrals with respect to an increasing process in the $G$-framework and extend $G$-It\^o's formula. Moreover, we study the solvability of the scalar valued stochastic differential…

Hybrid stochastic differential equations are a useful tool to model continuously varying stochastic systems which are modulated by a random environment that may depend on the system state itself. In this paper, we establish the pathwise…

Stochastic density functional theory is applied to analyze the conductivity of strong two species electrolytes at arbitrary field strengths. The corresponding stochastic equations for the density of the electrolyte species are solved by…

We consider discrete-time dynamical systems with a linear relaxation dynamics that are driven by deterministic chaotic forces. By perturbative expansion in a small time scale parameter, we derive from the Perron-Frobenius equation the…

We consider linear stochastic differential-algebraic equations with constant coefficients and additive white noise. Due to the nature of this class of equations, the solution must be defined as a generalised process (in the sense of Dawson…

This article aims to investigate sufficient conditions for the stability of stochastic differential equations with a random structure, particularly in contexts involving the presence of concentration points. The proof of asymptotic…

The accurate numerical solution of partial differential equations is a central task in numerical analysis allowing to model a wide range of natural phenomena by employing specialized solvers depending on the scenario of application. Here,…

We consider reflected generalized backward doubly stochastic differential equations driven by a non-homogeneous L\'evy process. Under stochastic conditions on the coefficients, we prove the existence and uniqueness of a solution.…

These notes rigorously construct the stochastic integral of a Hilbert Space valued process driven by a Cylindrical Brownian Motion. We expand upon this stochastic calculus to present an introduction to stochastic differential equations in…

We prove the path-by-path well-posedness of stochastic porous media and fast diffusion equations driven by linear, multiplicative noise. As a consequence, we obtain the existence of a random dynamical system. This solves an open problem…

Testing procedures for assessing specific parametric model forms, or for checking the plausibility of simplifying assumptions, play a central role in the mathematical treatment of the uncertain. No certain answers are obtained by testing…

Inspired by path-integral solutions to the quantum relaxation problem, we develop a numerical method to solve classical stochastic differential equations with multiplicative noise that avoids averaging over trajectories. To test the method,…

We propose to study a new type of Backward stochastic differential equations driven by a family of It\^o's processes. We prove existence and uniqueness of the solution, and investigate stability and comparison theorem.

We consider a mixed stochastic differential equation driven by possibly dependent fractional Brownian motion and Brownian motion. Under mild regularity assumptions on the coefficients, it is proved that the equation has a unique solution.

Logistic equations play a pivotal role in the study of any non linear evolution process exhibiting growth and saturation. The interest for the phenomenology, they rule, goes well beyond physical processes and cover many aspects of ecology,…

The aim of this paper is twofold. Firstly, we derive upper and lower non-Gaussian bounds for the densities of the marginal laws of the solutions to backward stochastic differential equations (BSDEs) driven by fractional Brownian motions.…

Infinite-dimensional stochastic differential equations (ISDEs) describing systems with an infinite number of particles are considered. Each particle undergoes a L\'evy process, and the interaction between particles is determined by the…

We consider slow-fast systems of differential equations, in which both the slow and fast variables are perturbed by noise. When the deterministic system admits a uniformly asymptotically stable slow manifold, we show that the sample paths…