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Fractional differential equations driven by Lévy noise

Author

Listed:
  • V. V. Anh
  • R. McVinish

Abstract

This paper considers a general class of fractional differential equations driven by Lévy noise. The singularity spectrum for these equations is obtained. This result allows to determine the conditions under which the solution is a semimartingale. The prediction formula and a numerical scheme for approximating the sample paths of these equations are given. Almost sure, uniform convergence of the scheme and some numerical results are also provided.

Suggested Citation

  • V. V. Anh & R. McVinish, 2003. "Fractional differential equations driven by Lévy noise," International Journal of Stochastic Analysis, Hindawi, vol. 16, pages 1-23, January.
    • Handle: RePEc:hin:jnijsa:539490
    DOI: 10.1155/S1048953303000078
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    Cited by:

    1. Zhi-Han Zhao & Yong-Kui Chang & Juan J. Nieto, 2013. "Asymptotic Behavior of Solutions to Abstract Stochastic Fractional Partial Integrodifferential Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    2. M. D. Qassim & K. M. Furati & N.-E. Tatar, 2012. "On a Differential Equation Involving Hilfer‐Hadamard Fractional Derivative," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).

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