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A Note on Limiting Behaviour of Disastrous Environment Exponents


 
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1. Title Title of document A Note on Limiting Behaviour of Disastrous Environment Exponents
 
2. Creator Author's name, affiliation, country Thomas S. Mountford; University of California, Los Angeles
 
3. Subject Discipline(s) Mathematics
 
3. Subject Keyword(s) Random walk, disaster point, Poisson process.
 
3. Subject Subject classification 60K35
 
4. Description Abstract We consider a random walk on the $d$-dimensional lattice and investigate the asymptotic probability of the walk avoiding a "disaster" (points put down according to a regular Poisson process on space-time). We show that, given the Poisson process points, almost surely, the chance of surviving to time $t$ is like $e^{-\alpha \log (\frac1k) t } $, as $t$ tends to infinity if $k$, the jump rate of the random walk, is small.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2001-01-05
 
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/74
 
10. Identifier Digital Object Identifier 10.1214/EJP.v6-74
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 6
 
12. Language English=en en
 
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