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

Carathéodory approximations and stability of solutions to non-Lipschitz stochastic fractional... 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Computation Elsevier

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

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Publisher
Elsevier
Copyright
Copyright © 2018 Elsevier Inc.
ISSN
0096-3003
eISSN
1873-5649
D.O.I.
10.1016/j.amc.2018.02.005
Publisher site
See Article on Publisher Site

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.

Journal

Applied Mathematics and ComputationElsevier

Published: Jul 15, 2018

References

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