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Contents of PMS, Vol. 43, Fasc. 1,
pages 1 - 21
DOI: 10.37190/0208-4147.00092
Published online 13.4.2023
 

Fractional stochastic differential equations driven by $G$-Brownian motion with delays

A. Saci
A. Redjil
H. Boutabia
O. Kebiri

Abstract:

This paper consists of two parts. In part I, existence and uniqueness of solution for fractional stochastic differential equations driven by G-Brownian motion with delays (G-FSDEs for short) is established. In part II, the averaging principle for this type of equations is given. We prove under some assumptions that the solution of G-FSDE can be approximated by solution of its averaged stochastic system in the sense of mean square.

2010 AMS Mathematics Subject Classification: Primary 60H05; Secondary 60H20, 34C29.

Keywords and phrases: non-linear expectation, $G$-Brownian motion, fractional calculus, averaging principle.

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