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Existence and Uniqueness of Solutions to Neutral Stochastic Functional Differential Equations with Poisson Jumps

Author

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  • Jianguo Tan
  • Hongli Wang
  • Yongfeng Guo

Abstract

A class of neutral stochastic functional differential equations with Poisson jumps (NSFDEwPJs), d [ x ( t ) - G ( x t ) ] = f ( x t , t ) d t + g ( x t , t ) d W ( t ) + h ( x t , t ) d N ( t ) , t ∈ [ t 0 , T ] , with initial value x t 0 = ξ = { ξ ( θ ) : - τ ≤ θ ≤ 0 } , is investigated. First, we consider the existence and uniqueness of solutions to NSFDEwPJs under the uniform Lipschitz condition, the linear growth condition, and the contractive mapping. Then, the uniform Lipschitz condition is replaced by the local Lipschitz condition, and the existence and uniqueness theorem for NSFDEwPJs is also derived.

Suggested Citation

  • Jianguo Tan & Hongli Wang & Yongfeng Guo, 2012. "Existence and Uniqueness of Solutions to Neutral Stochastic Functional Differential Equations with Poisson Jumps," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-20, July.
    • Handle: RePEc:hin:jnlaaa:371239
    DOI: 10.1155/2012/371239
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    Cited by:

    1. Haoyi Mo & Xueyan Zhao & Feiqi Deng, 2017. "Exponential mean-square stability of the θ-method for neutral stochastic delay differential equations with jumps," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(3), pages 462-470, February.
    2. Sheng Wang & Guixin Hu & Linshan Wang, 2018. "Stability in Distribution of a Stochastic Competitive Lotka-Volterra System with S-type Distributed Time Delays," Methodology and Computing in Applied Probability, Springer, vol. 20(4), pages 1241-1257, December.

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