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Cauchy Problem for a Stochastic Fractional Differential Equation with Caputo-Itô Derivative

Author

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  • Jorge Sanchez-Ortiz

    (Facultad de Matemáticas, Universidad Autónoma de Guerrero, Av. Lázaro Cárdenas S/N Cd, Universitaria, Chilpancingo, Guerrero C.P. 39087, Mexico
    These authors contributed equally to this work.)

  • Omar U. Lopez-Cresencio

    (Facultad de Matemáticas, Universidad Autónoma de Guerrero, Av. Lázaro Cárdenas S/N Cd, Universitaria, Chilpancingo, Guerrero C.P. 39087, Mexico
    These authors contributed equally to this work.)

  • Francisco J. Ariza-Hernandez

    (Facultad de Matemáticas, Universidad Autónoma de Guerrero, Av. Lázaro Cárdenas S/N Cd, Universitaria, Chilpancingo, Guerrero C.P. 39087, Mexico
    These authors contributed equally to this work.)

  • Martin P. Arciga-Alejandre

    (Facultad de Matemáticas, Universidad Autónoma de Guerrero, Av. Lázaro Cárdenas S/N Cd, Universitaria, Chilpancingo, Guerrero C.P. 39087, Mexico
    These authors contributed equally to this work.)

Abstract

In this note, we define an operator on a space of Itô processes, which we call Caputo-Itô derivative, then we considerer a Cauchy problem for a stochastic fractional differential equation with this derivative. We demonstrate the existence and uniqueness by a contraction mapping argument and some examples are given.

Suggested Citation

  • Jorge Sanchez-Ortiz & Omar U. Lopez-Cresencio & Francisco J. Ariza-Hernandez & Martin P. Arciga-Alejandre, 2021. "Cauchy Problem for a Stochastic Fractional Differential Equation with Caputo-Itô Derivative," Mathematics, MDPI, vol. 9(13), pages 1-10, June.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:13:p:1479-:d:581182
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    References listed on IDEAS

    as
    1. Kunita, Hiroshi, 2010. "Itô's stochastic calculus: Its surprising power for applications," Stochastic Processes and their Applications, Elsevier, vol. 120(5), pages 622-652, May.
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