Basic theory and stability analysis for neutral stochastic functional differential equations with pure jumps

Li, Mengling and Deng, Feiqi and Mao, Xuerong (2019) Basic theory and stability analysis for neutral stochastic functional differential equations with pure jumps. Science in China Series F - Information Sciences, 62. 12204. ISSN 1009-2757 (https://doi.org/10.1007/s11432-017-9302-9)

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Abstract

This paper investigates the existence and uniqueness of solutions to neutral stochastic functional differential equations with pure jumps (NSFDEwPJs). The boundedness and almost sure exponential stability are also considered. In general, the classical existence and uniqueness theorem of solutions can be obtained under a local Lipschitz condition and linear growth condition. However, there are many equations that do not obey the linear growth condition. Therefore, our first aim is to establish new theorems where the linear growth condition is no longer required whereas the upper bound for the diffusion operator will play a leading role. Moreover, the pth moment boundedness and almost sure exponential stability are also obtained under some loose conditions. Finally, we present two examples to illustrate the effectiveness of our results.

ORCID iDs

Li, Mengling, Deng, Feiqi and Mao, Xuerong ORCID logoORCID: https://orcid.org/0000-0002-6768-9864;
  • Item type:Article
    ID code:70507
    Dates:
    Date
    Event
    31 January 2019
    Published
    16 October 2018
    Published Online
    6 November 2017
    Accepted
    Subjects:Science > Mathematics
    Department:Faculty of Science > Mathematics and Statistics
    Depositing user: Pure Administrator
    Date deposited:14 Nov 2019 10:57
    Last modified:11 Nov 2024 12:30
    URI:https://strathprints.strath.ac.uk/id/eprint/70507
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