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

2013/10/09 by John A. D. Appleby, Appleby, John A. D., Huizhong Appleby-Wu +3
Economics, Econometrics and Finance · Mathematics · #Classical Analysis and ODEs (math.CA) #Differential Equations and Numerical Methods #FOS: Mathematics #Nonlinear Differential Equations Analysis #Probability (math.PR) #Stochastic processes and financial applications #math.CA #math.PR

paper · pdf · doi:10.48550/arxiv.1310.2352

35 pages

arxiv created 2013/10/09 · openalex publication_date 2013/10/09 · arxiv updated 2013/10/10 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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.

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