Impulsive stochastic fractional differential equations driven by fractional Brownian motion

Abstract

In this research, we study the existence and uniqueness results for a new class of stochastic fractional differential equations with impulses driven by a standard Brownian motion and an independent fractional Brownian motion with Hurst index 1/2 < H < 1 under a non-Lipschitz condition with the Lipschitz one as a particular case. Our analysis depends on an approximation scheme of Carathéodory type. Some previous results are improved and extended.

Existence and stability results for Caputo fractional stochastic differential equations with Lévy noise

“…The stability of nonlinear stochastic fractional dynamical system with Lévy noise is obtained using Mittag Leffler function. Further we can extend this results for stochastic impulsive systems with Lévy noise [2], stochastic neutral systems and stochastic delay integrodifferential systems.…”

Periodic averaging method for impulsive stochastic dynamical systems driven by fractional Brownian motion under non-Lipschitz condition

“…(2) is given by the following theorem. Proof The proof is a special case of the proof of Theorem 3.1 in Abouagwa et al [38] and easy to be derived. So, we omit the proof here.…”

Estimating Drift Parameters in a Sub-Fractional Vasicek-Type Process

“…for all t, v ≥ 0. Note that, when H = 1 2 , S H corresponds to the well known Brownian motion B. Sub-fractional Brownian motion has properties that are similar to those of fractional Brownian motion, such as the following: long-range dependence, Self-similarity, Hölder pathes, and it satisfies [17][18][19][20][21][22][23].…”