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Stationary distributions for stochastic differential equations with memory driven by α-stable processes

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  • Wang, Wei
  • Wang, Xiulian

Abstract

In this work, we consider the stationarity of a class of stochastic differential equations with memory driven by α-stable processes. Sufficient conditions are given to guarantee the existence and uniqueness of the stationary distribution for the stochastic system. Last, an example is given to illustrate the results.

Suggested Citation

  • Wang, Wei & Wang, Xiulian, 2023. "Stationary distributions for stochastic differential equations with memory driven by α-stable processes," Statistics & Probability Letters, Elsevier, vol. 195(C).
    • Handle: RePEc:eee:stapro:v:195:y:2023:i:c:s0167715222002796
    DOI: 10.1016/j.spl.2022.109766
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    References listed on IDEAS

    as
    1. Yuan, Chenggui & Mao, Xuerong, 2003. "Asymptotic stability in distribution of stochastic differential equations with Markovian switching," Stochastic Processes and their Applications, Elsevier, vol. 103(2), pages 277-291, February.
    2. Liu, Kai, 2020. "Stationary distributions of second order stochastic evolution equations with memory in Hilbert spaces," Stochastic Processes and their Applications, Elsevier, vol. 130(1), pages 366-393.
    3. Liu, Kai, 2019. "Stability in distribution for stochastic differential equations with memory driven by positive semigroups and Lévy processes," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.
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