Invariance of Brownian motion associated with exponential functionals

Yuu Hariya

Stochastic Processes and their Applications, 2024, vol. 167, issue C

Abstract: 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 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.

Keywords: Brownian motion; Exponential functional; Anticipative path transformation (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1016/j.spa.2023.104235

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