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On a Fractional SPDE Driven by Fractional Noise and a Pure Jump Lévy Noise in ℝd

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Listed:
  • Xichao Sun
  • Zhi Wang
  • Jing Cui

Abstract

We study a stochastic partial differential equation in the whole space x ∈ ℝd, with arbitrary dimension d ≥ 1, driven by fractional noise and a pure jump Lévy space‐time white noise. Our equation involves a fractional derivative operator. Under some suitable assumptions, we establish the existence and uniqueness of the global mild solution via fixed point principle.

Suggested Citation

  • Xichao Sun & Zhi Wang & Jing Cui, 2014. "On a Fractional SPDE Driven by Fractional Noise and a Pure Jump Lévy Noise in ℝd," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:758270
    DOI: 10.1155/2014/758270
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    References listed on IDEAS

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    1. Mémin, Jean & Mishura, Yulia & Valkeila, Esko, 2001. "Inequalities for the moments of Wiener integrals with respect to a fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 51(2), pages 197-206, January.
    2. Wu, Dongsheng, 2011. "On the solution process for a stochastic fractional partial differential equation driven by space-time white noise," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1161-1172, August.
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