Almost subadditive multiparameter ergodic theorems

Klaus Schürger

Stochastic Processes and their Applications, 1988, vol. 29, issue 2, 171-193

Abstract: The purpose of this paper is to extend recent mean as well as a.e. convergence results of Derriennic (1983), Liggett (1985) and Schürger (1986) to multiparameter processes X which satisfy a strong almost subadditivity condition and have certain monotonicity properties. If X is even strongly subadditive, we derive an a.e. limit theorem which extends Tempel'man's (1972) multiparameter pointwise ergodic theorem in the same way as Kingman's (1968) subadditive ergodic theorem extends Birkhoff's ergodic theorem (here, X is not supposed to have any monotonicity properties). We also point out how the results obtained can be used to arrive at analogous results for multiparameter random sets.

Keywords: L1-convergence; a.e.; convergence; multiparameter; subadditive; ergodic; theorem; travelling; salesman; problem; cluster; process; multiparameter; random; sets (search for similar items in EconPapers)
Date: 1988
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/0304-4149(88)90036-1
Full text for ScienceDirect subscribers only

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:eee:spapps:v:29:y:1988:i:2:p:171-193

Ordering information: This journal article can be ordered from
http://http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

Access Statistics for this article

Stochastic Processes and their Applications is currently edited by T. Mikosch

More articles in Stochastic Processes and their Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().