A trivariate version of 'Lévy's equivalence'

Gordon Simons

Statistics & Probability Letters, 1986, vol. 4, issue 1, 7-8

Abstract: It is shown that the trivariate stochastic processes {(Mt-Wt, Mt, [Theta]t), t >= 0} and {(Wt, Lt, Tt), t >= 0} have the same distributions when: W = {Wt, t >= 0} is a Wiener process, Mt is the maximum value attained by W over the time interval [0, t], [Theta]t is the time the maximum value is attained, Lt is the local time of W at level zero and time t, and Tt is the last time W is zero in the time interval [0, t]. A straightforward proof, based on 'Tanaka's formula, establishes this result by deriving an almost sure version of the equivalence.

Keywords: Wiener; process; Lévy's; equivalence; Tanaka's; formula (search for similar items in EconPapers)
Date: 1986
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