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Stochastic fractional evolution equations with fractional brownian motion and infinite delay

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  • Xu, Liping
  • Li, Zhi

Abstract

In this paper, we consider a class of stochastic fractional evolution equations with infinite delay and a fractional Brownian motion in a Hilbert space. By the stochastic analysis technique, we establish the existence and uniqueness of mild solutions for these equations under non-Lipschitz condition with Lipschitz conditions being considered as a special case. An example is provided to illustrate the theory.

Suggested Citation

  • Xu, Liping & Li, Zhi, 2018. "Stochastic fractional evolution equations with fractional brownian motion and infinite delay," Applied Mathematics and Computation, Elsevier, vol. 336(C), pages 36-46.
  • Handle: RePEc:eee:apmaco:v:336:y:2018:i:c:p:36-46
    DOI: 10.1016/j.amc.2018.04.060
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    1. Boufoussi, Brahim & Hajji, Salah, 2012. "Neutral stochastic functional differential equations driven by a fractional Brownian motion in a Hilbert space," Statistics & Probability Letters, Elsevier, vol. 82(8), pages 1549-1558.
    2. Fabienne Comte & Eric Renault, 1998. "Long memory in continuous‐time stochastic volatility models," Mathematical Finance, Wiley Blackwell, vol. 8(4), pages 291-323, October.
    3. Ingve Simonsen, 2001. "Measuring Anti-Correlations in the Nordic Electricity Spot Market by Wavelets," Papers cond-mat/0108033, arXiv.org, revised Apr 2003.
    4. Luo, Jiaowan & Liu, Kai, 2008. "Stability of infinite dimensional stochastic evolution equations with memory and Markovian jumps," Stochastic Processes and their Applications, Elsevier, vol. 118(5), pages 864-895, May.
    5. Comte, F. & Renault, E., 1996. "Long memory continuous time models," Journal of Econometrics, Elsevier, vol. 73(1), pages 101-149, July.
    6. Simonsen, Ingve, 2003. "Measuring anti-correlations in the nordic electricity spot market by wavelets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 322(C), pages 597-606.
    7. Röckner, Michael & Zhu, Rongchan & Zhu, Xiangchan, 2014. "Local existence and non-explosion of solutions for stochastic fractional partial differential equations driven by multiplicative noise," Stochastic Processes and their Applications, Elsevier, vol. 124(5), pages 1974-2002.
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