Electronic Journal of Probability

Existence and Exponential Mixing of Infinite White $\alpha$-Stable Systems with Unbounded Interactions

Lihu Xu and Boguslaw Zegarlinski

Full-text: Open access

Abstract

We study an infinite white $\alpha$-stable systems with unbounded interactions, and prove the existence of a solution by Galerkin approximation and an exponential mixing property by an $\alpha$-stable version of gradient bounds.

Article information

Source
Electron. J. Probab., Volume 15 (2010), paper no. 65, 1994-2018.

Dates
Accepted: 2 December 2010
First available in Project Euclid: 1 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1464819850

Digital Object Identifier
doi:10.1214/EJP.v15-831

Mathematical Reviews number (MathSciNet)
MR2745723

Zentralblatt MATH identifier
1221.37160

Subjects
Primary: 37L55: Infinite-dimensional random dynamical systems; stochastic equations [See also 35R60, 60H10, 60H15]
Secondary: 60H10: Stochastic ordinary differential equations [See also 34F05] 60H15: Stochastic partial differential equations [See also 35R60]

Keywords
Exponential mixing White symmetric $alpha$-stable processes Lie bracket Finite speed of propagation of information Gradient bounds

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Xu, Lihu; Zegarlinski, Boguslaw. Existence and Exponential Mixing of Infinite White $\alpha$-Stable Systems with Unbounded Interactions. Electron. J. Probab. 15 (2010), paper no. 65, 1994--2018. doi:10.1214/EJP.v15-831. https://projecteuclid.org/euclid.ejp/1464819850


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