Abstract
In [3], Kotani proved analytically that expectations for additive functionals of Brownian motion of the form have the asymptotics as for some suitable non-negative functions , and . 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 comes from the transition probability of 3-dimensional Bessel process.
Citation
Yuu HARIYA. "A time-change approach to Kotani's extension of Yor's formula." J. Math. Soc. Japan 58 (1) 129 - 151, JANUARY, 2006. https://doi.org/10.2969/jmsj/1145287096
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