Asymptotic behaviours of a stochastic delay equation driven by an fBm in Hilbert space. Issue 8 (17th November 2019)

• Record Type: Journal Article
• Authors: Yan, Litan; Yu, Xianye
• Is Part Of: Stochastics. Volume 91:Issue 8(2019)
• Page Start: 1164
• Page End: 1185
• Publication Date: 2019-11-17
• Subjects: Fractional Brownian motion -- controllability -- stochastic delay equations -- exponential stability; 34E15 -- 93B05 -- 93E15; Stochastic processes -- Periodicals; Probabilities -- Periodicals; 519.2
• DOI: 10.1080/17442508.2019.1577430
• Languages: English
• ISSNs: 1744-2508

Abstract

ABSTRACT: In this paper, we consider a class of stochastic delay equations in Hilbert spaces driven by fractional Brownian motion with Hurst parameter 1 2 ≤ H < 1 . We obtain a sufficient condition for controllability of the systems and prove that their mild solutions are exponentially stable in p th moment with p > 1 / H by using adequately the characteristic of fractional Brownian motion and the fractional power A α of a linear operator A with 0 < α < H . In particular, when 1 2 < H < 1 the mild solutions are exponentially stable in mean square.