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Random integrodifferential equations of Volterra type with delay : attractiveness and stability

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  • Diop, Amadou
  • Dieye, Moustapha
  • Hazarika, Bipan

Abstract

In this paper, the existence and the uniqueness of mild solutions of random integrodifferential equations are studied. To obtain random solutions, we develop a new tool in the resolvent operator theory and apply several fixed-point theorems. In addition, we establish the properties of mean-square stability and attractiveness. In the end, examples are worked out and we apply the theoretical outcomes to a type of the Heath-Jarrow-Morton-Musiela (HJMM) equation.

Suggested Citation

  • Diop, Amadou & Dieye, Moustapha & Hazarika, Bipan, 2022. "Random integrodifferential equations of Volterra type with delay : attractiveness and stability," Applied Mathematics and Computation, Elsevier, vol. 430(C).
    • Handle: RePEc:eee:apmaco:v:430:y:2022:i:c:s0096300322003757
    DOI: 10.1016/j.amc.2022.127301
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    References listed on IDEAS

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    1. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305, World Scientific Publishing Co. Pte. Ltd..
    2. Kazemi, M. & Yaghoobnia, A.R., 2022. "Application of fixed point theorem to solvability of functional stochastic integral equations," Applied Mathematics and Computation, Elsevier, vol. 417(C).
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