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The ruin problem and cover times of asymmetric random walks and Brownian motions

  • K. S. Chong (a1), Richard Cowan (a2) and Lars Holst (a3)
Abstract

A simple asymmetric random walk on the integers is stopped when its range is of a given length. When and where is it stopped? Analogous questions can be stated for a Brownian motion. Such problems are studied using results for the classical ruin problem, yielding results for the cover time and the range, both for asymmetric random walks and Brownian motion with drift.

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Corresponding author
Postal address: Department of Statistics, Chinese University of Hong Kong, Shatin, Hong Kong. Email address: kschong@hp735.sta.cuhk.edu.hk
∗∗ Postal address: School of Mathematics and Statistics, University of Sydney, NSW 2006, Australia. Email address: rcowan@mail.usyd.edu.au
∗∗∗ Postal address: Department of Mathematics, Royal Institute of Technology, SE 10044, Stockholm, Sweden. Email address: lholst@math.kth.se
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Advances in Applied Probability
  • ISSN: 0001-8678
  • EISSN: 1475-6064
  • URL: /core/journals/advances-in-applied-probability
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