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Acta Applicandae Mathematicae

, Volume 110, Issue 2, pp 627–638 | Cite as

The Existence and Uniqueness of the Solution for Neutral Stochastic Functional Differential Equations with Infinite Delay in Abstract Space

  • Yong XuEmail author
  • Shigeng Hu
Article

Abstract

The main aim of this paper is to prove the existence and uniqueness of the solution for neutral stochastic functional differential equations with infinite delay, which the initial data belong to the phase space ℬ((−∞,0];ℝ d ). The vital work of this paper is to extend the initial function space of the paper (Wei and Wang, J. Math. Anal. Appl. 331:516–531, 2007) and give some examples to show that the phase space ℬ((−∞,0];ℝ d ) exists. In addition, this paper builds a Banach space ℳ2((−∞,T],ℝ d ) with a new norm in order to discuss the existence and uniqueness of the solution for such equations with infinite delay.

Keywords

Phase space Neutral stochastic functional differential equations Infinite delay Existence Uniqueness 

Mathematics Subject Classification (2000)

34K40 60H10 

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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Department of MathematicsHuazhong University of Science and TechnologyWuhanChina

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