A time-change approach to Kotani's extension of Yor's formula

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In [3], Kotani proved analytically that expectations for additive functional of Brownian motion {Bt,t ≥ 0} of the form E0[f(B t)g(∫0φ(Bs)ds)] have the asymptotics t-3/2 as t → ∞ for some suitable non-negative functions φ f and g. This generalizes, in the asymptotic form, Yor's explicit formula [10] for exponential Brownian functionals. In the present paper, we discuss this generalization probabilistically, by using a time-change argument. We may easily see from our argument that this asymptotics t -3/2 comes from the transition probability of 3-dimensional Bessel process.

Original languageEnglish
Pages (from-to)129-151
Number of pages23
JournalJournal of the Mathematical Society of Japan
Issue number1
Publication statusPublished - 2006 Jan
Externally publishedYes


  • 3-dimensional Bessel processes
  • Additive functional of Brownian motion
  • Time-changes

ASJC Scopus subject areas

  • Mathematics(all)


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