Yuu Hariya
Published 2022-03-16Version 1
It is well known that Brownian motion enjoys several distributional invariances such as the scaling property and the time reversal. In this paper, we prove another invariance of Brownian motion that is compatible with the time reversal. The invariance, which seems to be new to our best knowledge, is described in terms of an anticipative path transformation involving exponential functionals as anticipating factors. Some related results are also provided.
Exponential functionals of Brownian motion and class-one Whittaker functions
Exponential functionals of Brownian motion, II: Some related diffusion processes
On some identities in law involving exponential functionals of Brownian motion and Cauchy variable
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