Zhang X, Ruan D. Exponential stability for neutral stochastic functional partial differential equations driven by Brownian motion and fractional Brownian motion.
JOURNAL OF INEQUALITIES AND APPLICATIONS 2018;
2018:201. [PMID:
30839575 PMCID:
PMC6096910 DOI:
10.1186/s13660-018-1793-9]
[Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 12/20/2017] [Accepted: 07/15/2018] [Indexed: 06/09/2023]
Abstract
In this paper, we study the exponential stability in the pth moment of mild solutions to neutral stochastic functional partial differential equations driven by Brownian motion and fractional Brownian motion: d [ x ( t ) + g ( t , x t ) ] = [ A x ( t ) + f ( t , x t ) ] d t + h ( t , x t ) d W ( t ) + σ ( t ) d B H ( t ) , where H ∈ ( 1 / 2 , 1 ) . Our method for investigating the stability of solutions is based on the Banach fixed point theorem. The obtained results generalize and improve the results due to Boufoussi and Hajji (Stat. Probab. Lett. 82:1549-1558, 2012), Caraballo et al. (Nonlinear Anal. 74:3671-3684, 2011), and Luo (J. Math. Anal. Appl. 355:414-425, 2009).
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