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

Jorge Sanchez-Ortiz, Omar U. Lopez-Cresencio, Francisco J. Ariza-Hernandez and Martin P. Arciga-Alejandre
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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
Omar U. Lopez-Cresencio: Facultad de Matemáticas, Universidad Autónoma de Guerrero, Av. Lázaro Cárdenas S/N Cd, Universitaria, Chilpancingo, Guerrero C.P. 39087, Mexico
Francisco J. Ariza-Hernandez: Facultad de Matemáticas, Universidad Autónoma de Guerrero, Av. Lázaro Cárdenas S/N Cd, Universitaria, Chilpancingo, Guerrero C.P. 39087, Mexico
Martin P. Arciga-Alejandre: Facultad de Matemáticas, Universidad Autónoma de Guerrero, Av. Lázaro Cárdenas S/N Cd, Universitaria, Chilpancingo, Guerrero C.P. 39087, Mexico

Mathematics, 2021, vol. 9, issue 13, 1-10

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.

Keywords: brownian motion; Caputo-Itô derivative; Itô process; existence; uniqueness (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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