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Invariance of Brownian motion associated with exponential functionals

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  • Hariya, Yuu

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.

Suggested Citation

  • Hariya, Yuu, 2024. "Invariance of Brownian motion associated with exponential functionals," Stochastic Processes and their Applications, Elsevier, vol. 167(C).
    • Handle: RePEc:eee:spapps:v:167:y:2024:i:c:s0304414923002077
    DOI: 10.1016/j.spa.2023.104235
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    References listed on IDEAS

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    1. Donati-Martin, Catherine & Matsumoto, Hiroyuki & Yor, Marc, 2000. "On positive and negative moments of the integral of geometric Brownian motions," Statistics & Probability Letters, Elsevier, vol. 49(1), pages 45-52, August.
    2. Hariya, Yuu, 2022. "Extensions of Bougerol’s identity in law and the associated anticipative path transformations," Stochastic Processes and their Applications, Elsevier, vol. 146(C), pages 311-334.
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