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

Saci Akram, Redjil Amel, Boutabia Hacene, Kebiri Omar

Probability and Mathematical Statistics

2023

Vol. 43, Fasc. 1

1--21

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.

Chaotic expansion in the G-expectation space

Boutabia H., Grabsia I.

Opuscula Mathematica

2013

Vol. 33, no. 4

647--666

In this paper, we are motivated by uncertainty problems in volatility. We prove the equivalent theorem of Wiener chaos with respect to G-Brownian motion in the framework of a sublinear expectation space. Moreover, we establish some relationship between Hermite polynomials and G-stochastic multiple integrals. An equivalent of the orthogonality of Wiener chaos was found.