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

John A. D. Appleby, Huizhong Appleby-Wu, Xuerong Mao

Published 2013-10-09Version 1

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.