 Applications of the continuous-time ballot theorem to Brownian motion and related processesJason Schweinsberg Stochastic Processes and their Applications, 2001, vol. 95, issue 1, 151-176 Abstract: Motivated by questions related to a fragmentation process which has been studied by Aldous, Pitman, and Bertoin, we use the continuous-time ballot theorem to establish some results regarding the lengths of the excursions of Brownian motion and related processes. We show that the distribution of the lengths of the excursions below the maximum for Brownian motion conditioned to first hit [lambda]>0 at time t is not affected by conditioning the Brownian motion to stay below a line segment from (0,c) to (t,[lambda]). We extend a result of Bertoin by showing that the length of the first excursion below the maximum for a negative Brownian excursion plus drift is a size-biased pick from all of the excursion lengths, and we describe the law of a negative Brownian excursion plus drift after this first excursion. We then use the same methods to prove similar results for the excursions of more general Markov processes. Keywords: Fragmentation; processes; Ballot; theorem; Brownian; motion; Brownian; excursion (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:95:y:2001:i:1:p:151-176 Ordering information: This journal article can be ordered from Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
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