Distribution of the smallest visited point in a greedy walk on the line
2016 (English)In: Journal of Applied Probability, ISSN 0021-9002, E-ISSN 1475-6072, Vol. 53, no 3, 880-887 p.Article in journal (Refereed) Published
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.
Place, publisher, year, edition, pages
2016. Vol. 53, no 3, 880-887 p.
Probability Theory and Statistics
IdentifiersURN: urn:nbn:se:uu:diva-305791DOI: 10.1017/jpr.2016.46ISI: 000386349900016OAI: oai:DiVA.org:uu-305791DiVA: diva2:1039178