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

概要

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In [3], Kotani proved analytically that expectations for additive functionals of Brownian motion {Bt, t≥0} of the form E0 [ f(Bt)g (∫t0 φ(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, Yors 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.
社団法人日本数学会の論文
2006-01-01