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Controlled random walk with a target site


 
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1. Title Title of document Controlled random walk with a target site
 
2. Creator Author's name, affiliation, country Kenneth S. Alexander; University of Southern California; United States
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) random walk, stochastic control
 
3. Subject Subject classification 60G50; 93E20
 
4. Description Abstract We consider a symmetric simple random walk $\{W_i\}$ on $\mathbb{Z}^d, d=1,2$, in which the walker may choose to stand still for a limited time.  The time horizon is $n$, the maximum consecutive time steps which can be spent standing still is $m_n$ and the goal is to maximize $\mathbb{P}(W_n=0)$.  We show that for $d=1$, if $m_n \gg (\log n)^{2+\gamma}$ for some $\gamma>0$, there is a strategy for each $n$ yielding $\mathbb{P}(W_n = 0) \to 1$.  For $d=2$, if $m_n \gg n^\epsilon$ for some $\epsilon>0$ then there are strategies yielding $\liminf_n \mathbb{P}(W_n=0)>0$.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) NSF grant DMS-0804934
 
7. Date (YYYY-MM-DD) 2013-06-06
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/2763
 
10. Identifier Digital Object Identifier 10.1214/ECP.v18-2763
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 18
 
12. Language English=en en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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