Existence, uniqueness and almost surely asymptotic estimations of the solutions to neutral stochastic functional differential equations driven by pure jumps

Wei Mao, Quanxin Zhu, Xuerong Mao

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Abstract

In this paper, we are concerned with neutral stochastic functional differential equations driven by pure jumps (NSFDEwPJs). We prove the existence and uniqueness of the solution to NSFDEwPJs whose coefficients satisfying the Local Lipschitz condition. In addition, we establish the p-th exponential estimations and almost surely asymptotic estimations of the solution for NSFDEwJs
Original languageEnglish
Number of pages28
JournalApplied Mathematics and Computation
Publication statusAccepted/In press - 29 Dec 2014

Keywords

  • neutral stochastic functional differential equations
  • pure jumps
  • existence and uniqueness
  • exponential estimations
  • almost surely asymptotic estimations

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