Electronic Communications in Probability

Asymptotic behavior for neutral stochastic partial differential equations with infinite delays

Jing Cui and Litan Yan

Full-text: Open access

Abstract

This paper is concerned with the existence and asymptotic behavior of mild solutions to a class of non-linear neutral stochastic partial differential equations with infinite delays. By applying fixed point principle, we present sufficient conditions to ensure that the mild solutions are exponentially stable in $p$th-moment ($p\geq 2$) and almost surely exponentially stable. An example is provided to illustrate the effectiveness of the proposed result.

Article information

Source
Electron. Commun. Probab., Volume 18 (2013), paper no. 45, 12 pp.

Dates
Accepted: 8 June 2013
First available in Project Euclid: 7 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465315584

Digital Object Identifier
doi:10.1214/ECP.v18-2858

Mathematical Reviews number (MathSciNet)
MR3070911

Zentralblatt MATH identifier
1297.93173

Subjects
Primary: 93E15: Stochastic stability
Secondary: 34K50: Stochastic functional-differential equations [See also , 60Hxx] 60H15: Stochastic partial differential equations [See also 35R60]

Keywords
Neutral stochastic partial differential equations exponential stability infinite delay

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

Cui, Jing; Yan, Litan. Asymptotic behavior for neutral stochastic partial differential equations with infinite delays. Electron. Commun. Probab. 18 (2013), paper no. 45, 12 pp. doi:10.1214/ECP.v18-2858. https://projecteuclid.org/euclid.ecp/1465315584


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