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September 2016 Distribution of the smallest visited point in a greedy walk on the line
Katja Gabrysch
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J. Appl. Probab. 53(3): 880-887 (September 2016).

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.

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Katja Gabrysch. "Distribution of the smallest visited point in a greedy walk on the line." J. Appl. Probab. 53 (3) 880 - 887, September 2016.

Information

Published: September 2016
First available in Project Euclid: 13 October 2016

zbMATH: 1351.60060
MathSciNet: MR3570100

Subjects:
Primary: 60G55
Secondary: 60K35

Keywords: greedy walk , Poisson point process

Rights: Copyright © 2016 Applied Probability Trust

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Vol.53 • No. 3 • September 2016
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