Path Collapse for an Inhomogeneous Random Walk

Ilie Grigorescu, Min Kang

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


On an open interval we follow the paths of a Brownian motion which returns to a fixed point as soon as it reaches the boundary and restarts afresh indefinitely. We determine that two paths starting at different points either cannot collapse or they do so almost surely. The problem can be modelled as a spatially inhomogeneous random walk on a group and contrasts sharply with the higher dimensional case in that if two paths may collapse they do so almost surely.

Original languageEnglish (US)
Pages (from-to)147-159
Number of pages13
JournalJournal of Theoretical Probability
Issue number1
StatePublished - Jan 2003


  • Absorbing Brownian motion
  • Inhomogeneous random walks
  • Recurrence

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics(all)
  • Statistics, Probability and Uncertainty


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