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Heuristic approach to some laws for Brownian motion
Author(s) -
Imhof J. P.
Publication year - 1987
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3314917
Subject(s) - brownian motion , mathematics , brownian bridge , limit (mathematics) , random walk , statistical physics , brownian excursion , equivalence (formal languages) , law , geometric brownian motion , mathematical analysis , diffusion process , physics , statistics , computer science , discrete mathematics , knowledge management , innovation diffusion , political science
Abstract Csàki and Vincze have shown that for an elementary tied‐down random walk, the pair (maximum, instant of maximum) has the same law as (time spent in (0, 1/2), time spent above 1/2). Formal passage to the limit indicates that the former pair has for a Brownian bridge the same law as (local time at 0, duration of positivity). A quadrivariate density of Karatzas and Shreve and an equivalence for Brownian motion with drift follow.