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

Mathematics

Francisco J. Ariza-Hernandez¹  Jorge Sanchez-Ortiz¹  Omar U. Lopez-Cresencio¹  Martin P. Arciga-Alejandre¹ 

[1] Facultad de Matemáticas, Universidad Autónoma de Guerrero, Av. Lázaro Cárdenas S/N Cd, Universitaria, Chilpancingo, Guerrero C.P. 39087, Mexico;

关键词: brownian motion;    Caputo-Itô derivative;    Itô process;    existence;    uniqueness;   

DOI  :  10.3390/math9131479

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown