Controllability of neutral stochastic evolution equations driven by fBm with Hurst parameter less than 1/2

ABSTRACT

In this paper, we investigate the controllability for a class of neutral stochastic evolution equations driven by fractional Brownian motion with Hurst parameter $H\in (0,1/2)$ in a Hilbert space. By using the stochastic analysis of fractional Brown motion with Hurst parameter $H\in (0,1/2)$, the properties of operator semigroup and the Banach fixed point theorem, the sufficient conditions for the controllability of the considered equations are obtained. In the end, one example is given to illustrate the feasibility and effectiveness of the obtained results.

KEYWORDS:

• Controllability
• neutral stochastic evolution equations
• fractional Brownian motion

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 60H15
• 60G15
• 60H05

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research is partially supported by the NNSF of China (no. 11571071) and Natural Science Foundation of Hubei Province (no. 2016CFB479).