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Excursions and Local Limit Theorems for Bessel-like Random Walks


 
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1. Title Title of document Excursions and Local Limit Theorems for Bessel-like Random Walks
 
2. Creator Author's name, affiliation, country Kenneth S. Alexander; University of Southern California; United States
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) excursion, Lamperti problem, random walk, Bessel process
 
3. Subject Subject classification 60J10; 60J80
 
4. Description Abstract We consider reflecting random walks on the nonnegative integers with drift of order $1/x$ at height $x$. We establish explicit asymptotics for various probabilities associated to such walks, including the distribution of the hitting time of $0$ and first return time to $0$, and the probability of being at a given height at a given time (uniformly in a large range of heights.) In particular, for certain drifts inversely proportional to $x$ up to smaller-order correction terms, we show that the probability of a first return to $0$ at time $n$ decays as a certain inverse power of $n$, multiplied by a slowly varying factor that depends on the drift correction terms.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) NSF
 
7. Date (YYYY-MM-DD) 2011-01-02
 
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/848
 
10. Identifier Digital Object Identifier 10.1214/EJP.v16-848
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 16
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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