A variation of constant formula for Caputo fractional stochastic differential equations

Publication date: Available online 15 October 2018Source: Statistics & Probability LettersAuthor(s): P.T. Anh, T.S. Doan, P.T. HuongAbstractWe 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).

Source: Statistics and Probability Letters - October 16, 2018 Category: Statistics Source Type: research