Self-stabilizing Processes in Multi-wells Landscape in ℝ d -Invariant Probabilities

Julian Tugaut ()
Additional contact information
Julian Tugaut: Universität Bielefeld

Journal of Theoretical Probability, 2014, vol. 27, issue 1, 57-79

Abstract: Abstract The aim of this work is to analyze the stationary measures for a particular class of non-Markovian diffusions, the self-stabilizing processes. All the trajectories of such a process attract each other. This permits to exhibit a non-uniqueness of the stationary measures in the one-dimensional case, see Herrmann and Tugaut (Stoch. Process. Their Appl. 120(7):1215–1246, 2010). In this paper, the extension to general multi-wells lansdcape in general dimension is provided. Moreover, the approach for investigating this problem is different and needs fewer assumptions. The small-noise limit behavior of the invariant probabilities is also given.

Keywords: Self-interacting diffusion; Free-energy; McKean–Vlasov stochastic differential equations; Stationary measures; Uniqueness problem; Granular media equation; 60H10; 35K55; 60J60; 60G10; 41A60 (search for similar items in EconPapers)
Date: 2014
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10959-012-0435-2 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:27:y:2014:i:1:d:10.1007_s10959-012-0435-2

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

DOI: 10.1007/s10959-012-0435-2

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 ().