Row finite systems of stochastic differential equations with dissipative drift

TL;DR

This paper investigates infinite systems of stochastic differential equations with dissipative drift, establishing existence and uniqueness of solutions using finite volume approximation and the Ovsjannikov method, motivated by non-equilibrium spin dynamics.

Contribution

It introduces a novel approach to prove existence and uniqueness for infinite stochastic systems with dissipative drift, extending previous finite-dimensional results.

Findings

Proved existence of solutions for infinite stochastic systems.

Established uniqueness of solutions under dissipative conditions.

Applied finite volume approximation and Ovsjannikov method effectively.

Abstract

Motivated by studies of stochastic systems describing non-equilibrium dynamics of (real-valued) spins of an infinite particle system in $\mathbb{R}^n$ we consider a row-finite system of stochastic differential equations with dissipative drift. The existence and uniqueness of infinite time solutions is proved via finite volume approximation and a version of the Ovsjannikov method.