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Distribution of the smallest visited point in a greedy walk on the line

Part of: Stochastic processes Special processes

Published online by Cambridge University Press:  24 October 2016

Katja Gabrysch
Katja Gabrysch*
Affiliation:
Uppsala University
*
* Postal address: Department of Mathematics, Uppsala University, PO Box 480, 751 06 Uppsala, Sweden. Email address: katja.gabrysch@math.uu.se
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Abstract

We consider a greedy walk on a Poisson process on the real line. It is known that the walk does not visit all points of the process. In this paper we first obtain some useful independence properties associated with this process which enable us to compute the distribution of the sequence of indices of visited points. Given that the walk tends to +∞, we find the distribution of the number of visited points in the negative half-line, as well as the distribution of the time at which the walk achieves its minimum.

Keywords

Poisson point processgreedy walk

MSC classification

Primary: 60G55: Point processes
Secondary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 53 , Issue 3 , September 2016 , pp. 880 - 887
Copyright
Copyright © Applied Probability Trust 2016 

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References

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