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Fractional stochastic Volterra equation perturbed by fractional Brownian motion

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  • Zhang, Yinghan
  • Yang, Xiaoyuan

Abstract

In this paper, we consider a class of fractional stochastic Volterra equation of convolution type driven by infinite dimensional fractional Brownian motion with Hurst index h∈(0,1). Base on the explicit formula for the scalar resolvent function and the properties of the Mittag–Leffler’s function, the existence and regularity results of the stochastic convolution process are established. Separate proofs are required for the cases of Hurst parameter above and below 12 and it will turn out that the regularity of the solution increases with Hurst parameter h.

Suggested Citation

  • Zhang, Yinghan & Yang, Xiaoyuan, 2015. "Fractional stochastic Volterra equation perturbed by fractional Brownian motion," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 20-36.
    • Handle: RePEc:eee:apmaco:v:256:y:2015:i:c:p:20-36
    DOI: 10.1016/j.amc.2015.01.046
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    References listed on IDEAS

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    1. Hu, Yaozhong & Nualart, David & Song, Xiaoming, 2008. "A singular stochastic differential equation driven by fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 78(14), pages 2075-2085, October.
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    6. B. Pasik-Duncan & T. E. Duncan & B. Maslowski, 2006. "Linear Stochastic Equations in a Hilbert Space with a Fractional Brownian Motion," International Series in Operations Research & Management Science, in: Houmin Yan & George Yin & Qing Zhang (ed.), Stochastic Processes, Optimization, and Control Theory: Applications in Financial Engineering, Queueing Networks, and Manufacturing Systems, chapter 0, pages 201-221, Springer.
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