 Collision times and exit times from cones: a dualityNeil O'Connell and Antony Unwin Stochastic Processes and their Applications, 1992, vol. 43, issue 2, 291-301 Abstract: We consider the first collision time for a set of independent one-dimensional zero-drift Wiener processes. For the 3-process problem, the first collision time corresponds to the first exit time of Brownian motion in a cone in 2, and we can apply the results of Spitzer (1958) and Dante DeBlassie (1987) to obtain its distribution. In the case where the processes have equal infinitesimal variance, a more elementary method yields nice closed-form results for the 3-process problem, and second order approximations for the general n-process problem. This case (for three processes) corresponds to Brownian motion in a cone of angle [pi]. The latter approach can in fact be applied to any system of independent (identical) Markov processes, provided the single-barrier hitting time distributions are known for the individual processes and their differences, and provided the processes can't jump over each other. Keywords: first; exit; times; collision; times; particle; systems; cones (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:43:y:1992:i:2:p:291-301 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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