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Abstract semilinear stochastic Itó-Volterra integrodifferential equations

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  • David N. Keck
  • Mark A. McKibben

Abstract

We consider a class of abstract semilinear stochastic Volterra integrodifferential equations in a real separable Hilbert space. The global existence and uniqueness of a mild solution, as well as a perturbation result, are established under the so-called Caratheodory growth conditions on the nonlinearities. An approximation result is then established, followed by an analogous result concerning a so-called McKean-Vlasov integrodifferential equation, and then a brief commentary on the extension of the main results to the time-dependent case. The paper ends with a discussion of some concrete examples to illustrate the abstract theory.

Suggested Citation

  • David N. Keck & Mark A. McKibben, 2006. "Abstract semilinear stochastic Itó-Volterra integrodifferential equations," International Journal of Stochastic Analysis, Hindawi, vol. 2006, pages 1-22, July.
    • Handle: RePEc:hin:jnijsa:045253
    DOI: 10.1155/JAMSA/2006/45253
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    Cited by:

    1. Deya, Aurélien & Tindel, Samy, 2011. "Rough Volterra equations 2: Convolutional generalized integrals," Stochastic Processes and their Applications, Elsevier, vol. 121(8), pages 1864-1899, August.

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