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A variation of constant formula for Caputo fractional stochastic differential equations with jump–diffusion

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  • Xu, Shuli
  • Feng, Yuqiang
  • Jiang, Jun
  • Nie, Na

Abstract

In this paper, the existence and uniqueness of solutions for the Caputo fractional stochastic differential equations with jump–diffusion is discussed. Then, a variation of constant formula for the equation is established. The main ingredient of the proof is to use Itoˆ’s isometry of Poisson jumps and martingale representation theorem.

Suggested Citation

  • Xu, Shuli & Feng, Yuqiang & Jiang, Jun & Nie, Na, 2022. "A variation of constant formula for Caputo fractional stochastic differential equations with jump–diffusion," Statistics & Probability Letters, Elsevier, vol. 185(C).
    • Handle: RePEc:eee:stapro:v:185:y:2022:i:c:s016771522200027x
    DOI: 10.1016/j.spl.2022.109406
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    References listed on IDEAS

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    1. Ahmadova, Arzu & Mahmudov, Nazim I., 2020. "Existence and uniqueness results for a class of fractional stochastic neutral differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    2. Philippe Jorion, 1988. "On Jump Processes in the Foreign Exchange and Stock Markets," The Review of Financial Studies, Society for Financial Studies, vol. 1(4), pages 427-445.
    3. Anh, P.T. & Doan, T.S. & Huong, P.T., 2019. "A variation of constant formula for Caputo fractional stochastic differential equations," Statistics & Probability Letters, Elsevier, vol. 145(C), pages 351-358.
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    Cited by:

    1. Li, Min & Huang, Chengming & Wang, Nan, 2024. "A variation of constant formula for Caputo–Hadamard fractional stochastic differential equations⋆," Statistics & Probability Letters, Elsevier, vol. 214(C).

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