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A Note on Limiting Behaviour of Disastrous Environment Exponents

   
@article{EJP74,
	author = {Thomas Mountford},
	title = {A Note on Limiting Behaviour of Disastrous Environment Exponents},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {6},
	year = {2001},
	keywords = {Random walk, disaster point, Poisson process.},
	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.},
	pages = {no. 1, 1-10},
	issn = {1083-6489},
	doi = {10.1214/EJP.v6-74},    
        url = {http://ejp.ejpecp.org/article/view/74}}