On the Existence and Uniqueness of Solutions of Stochastic Equations of Neutral Type

TL;DR

This paper investigates the conditions under which strong solutions to stochastic neutral functional differential equations exist and are unique, relaxing traditional assumptions and providing growth rate estimates.

Contribution

It introduces weaker conditions for existence and uniqueness of solutions to stochastic neutral equations, aligning them with those used for deterministic cases.

Findings

Weaker conditions ensure existence and uniqueness of solutions.

Exponential growth estimates for solutions are derived.

Results apply to important classes of functional differential equations.

Abstract

This paper considers some the existence and uniqueness of strong solutions of stochastic neutral functional differential equations. The conditions on the neutral functional relax those commonly used to establish the existence and uniqueness of solutions of NSFDEs for many important classes of functional, and parallel the conditions used to ensure existence and uniqueness of solutions of related deterministic neutral equations. Exponential estimates on the almost sure and p--th mean rate of growth of solutions under the weaker existence conditions are also given.