A variation of constant formula for Caputo fractional stochastic differential equations

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 determinis...

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Bibliographic Details
Published in:Statistics & probability letters 2019-02, Vol.145, p.351-358
Main Authors: Anh, P.T., Doan, T.S., Huong, P.T.
Format: Article
Language:English
Subjects:
A variation of constant formula
Classical solution
Fractional stochastic differential equations
Inhomogeneous linear systems
Mild solution
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Summary: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).
ISSN:0167-7152
1879-2103
DOI:10.1016/j.spl.2018.10.010