Asymptotic Behavior of Stochastic Complex Lattice Systems Driven by Superlinear Noise

Zhang Chen () and Bixiang Wang ()
Additional contact information
Zhang Chen: Shandong University
Bixiang Wang: New Mexico Institute of Mining and Technology

Journal of Theoretical Probability, 2023, vol. 36, issue 3, 1487-1519

Abstract: Abstract This paper deals with the asymptotic behavior of complex stochastic lattice systems driven by superlinear noise. We first prove the well-posedness and the existence of weak mean random attractors of the systems. We then show the existence of periodic measures and the weak compactness of the set of all periodic measures when a parameter varies in a bounded interval. We finally examine the limiting behavior of the periodic measures and in particular prove that every limit of periodic measures of the stochastic Ginzburg–Landau lattice system must be a periodic measure of the stochastic Schrödinger lattice system.

Keywords: Complex lattice system; Superlinear noise; Limit measure; Periodic measure; Weak mean random attractor; Tightness; 37L40; 37L55; 60H10 (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10959-022-01206-9 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jotpro:v:36:y:2023:i:3:d:10.1007_s10959-022-01206-9

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10959

DOI: 10.1007/s10959-022-01206-9

Access Statistics for this article

Journal of Theoretical Probability is currently edited by Andrea Monica

More articles in Journal of Theoretical Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().