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Non-homogeneous random walks with non-integrable increments and heavy-tailed random walks on strips

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Non-homogeneous random walks with non-integrable increments and heavy-tailed random walks on strips
2.	Creator	Author's name, affiliation, country	Ostap Hryniv; University of Durham; United Kingdom
2.	Creator	Author's name, affiliation, country	Iain M. MacPhee; University of Durham; United Kingdom
2.	Creator	Author's name, affiliation, country	Mikhail V. Menshikov; University of Durham; United Kingdom
2.	Creator	Author's name, affiliation, country	Andrew R. Wade; University of Strathclyde; United Kingdom
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Heavy-tailed random walks; non-homogeneous random walks; transience; rate of escape; passage times; last exit times; semimartingales; random walks on strips; random walks with internal degrees of freedom; risk process
3.	Subject	Subject classification	60G07; 60J05 (Primary) 60F15; 60G17; 60G50; 91B30 (Secondary)
4.	Description	Abstract	We study asymptotic properties of spatially non-homogeneous random walks with non-integrable increments, including transience, almost-sure bounds, and existence and non existence of moments for first-passage and last-exit times. In our proofs we also make use of estimates for hitting probabilities and large deviations bounds. Our results are more general than existing results in the literature, which consider only the case of sums of independent (typically, identically distributed) random variables. We do not assume the Markov property. Existing results that we generalize include a circle of ideas related to the Marcinkiewicz-Zygmund strong law of large numbers, as well as more recent work of Kesten and Maller. Our proofs are robust and use martingale methods. We demonstrate the benefit of the generality of our results by applications to some non-classical models, including random walks with heavy-tailed increments on two-dimensional strips, which include, for instance, certain generalized risk processes.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	2012-08-02
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ejp.ejpecp.org/article/view/2216
10.	Identifier	Digital Object Identifier	10.1214/EJP.v17-2216
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 17
12.	Language	English=en	en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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