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On A Brownian Motion Problem of T. Salisbury
Published online by Cambridge University Press: 20 November 2018
Abstract
Let B be a Brownian motion on R, B(0) = 0, and let f (t, x) be continuous. T. Salisbury conjectured that if the total variation of f (t, B(t)), 0 ≤ t ≤ 1, is finite P-a.s., then f does not depend on x. Here we prove that this is true if the expected total variation is finite.
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- Copyright © Canadian Mathematical Society 1997
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