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

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

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 exa...

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Bibliographic Details
Main Authors: Jorge Sanchez-Ortiz, Omar U. Lopez-Cresencio, Francisco J. Ariza-Hernandez, Martin P. Arciga-Alejandre
Format: Article
Language:English
Published: MDPI AG 2021-06-01
Series:Mathematics
Subjects:
brownian motion
Caputo-Itô derivative
Itô process
existence
uniqueness
Online Access:https://www.mdpi.com/2227-7390/9/13/1479
Description
Summary: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.
ISSN:2227-7390

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