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Rate of growth of a transient cookie random walk


 
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1. Title Title of document Rate of growth of a transient cookie random walk
 
2. Creator Author's name, affiliation, country Anne-Laure Basdevant; Université Paris VI
 
2. Creator Author's name, affiliation, country Arvind Singh; Université Paris VI
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Rates of transience; cookie or multi-excited random walk; branching process with migration
 
3. Subject Subject classification 60K35; 60J80; 60F05
 
4. Description Abstract We consider a one-dimensional transient cookie random walk. It is known from a previous paper (BS2008) that a cookie random walk $(X_n)$ has positive or zero speed according to some positive parameter $\alpha >1$ or $\leq 1$. In this article, we give the exact rate of growth of $X_n$ in the zero speed regime, namely: for $0<\alpha<1$, $X_n/n^{(α+1)/2}$ converges in law to a Mittag-Leffler distribution whereas for $\alpha=1$, $X_n(\log n)/n$ converges in probability to some positive constant.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2008-05-07
 
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/498
 
10. Identifier Digital Object Identifier 10.1214/EJP.v13-498
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 13
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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