Carathéodory approximations and stability of solutions to non-Lipschitz stochastic fractional differential equations of Itô-Doob type

Mahmoud Abouagwa, Jicheng Liu and Ji Li

Applied Mathematics and Computation, 2018, vol. 329, issue C, 143-153

Abstract: The existence and uniqueness theorem of solutions provides an effective tool for the model validation of both deterministic and stochastic equations. The objective of this paper is to establish the existence and uniqueness of solutions for a class of Itô-Doob stochastic fractional differential equations under non-Lipschitz condition which is weaker than Lipschitz one and contains it as a special case. The solution is constructed with the aid of Carathéodory approximation. Moreover, the continuous dependence of solutions on the initial value is investigated in view of the stability of solutions in the sense of mean square. Finally, an example is given to illustrate the theory.

Keywords: Non-Lipschitz condition; Carathéodory approximation; Stability; Fractional calculus; Stochastic differential equations (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:329:y:2018:i:c:p:143-153

DOI: 10.1016/j.amc.2018.02.005

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