A variation of constant formula for Caputo fractional stochastic differential equations

• Published in: Statistics & probability letters Vol. 145; pp. 351 - 358
• Main Authors: Anh, P.T., Doan, T.S., Huong, P.T.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.02.2019
• Subjects: A variation of constant formula; Classical solution; Fractional stochastic differential equations; Inhomogeneous linear systems; Mild solution; Fractional stochastic differential equations; Mild solution; Classical solution; A variation of constant formula; Inhomogeneous linear systems
• ISSN: 0167-7152; 1879-2103
• DOI: 10.1016/j.spl.2018.10.010

We establish and prove a variation of constant formula for Caputo fractional stochastic differential equations whose coefficients satisfy a standard Lipschitz condition. The main ingredient in the proof is to use Ito’s representation theorem and the known variation of constant formula for deterministic Caputo fractional differential equations. As a consequence, for these systems we point out the coincidence between the notion of classical solutions introduced in Wang et al. (2016) and mild solutions introduced in Sakthivel et al. (2013).