Summary
The scaling property of Brownian motion is exploited systematically in order to extend Paul Lévy's arc sine law to Brownian motion perturbed by its local time at 0. Other important ingredients of the proofs are some Ray-Knight theorems for local times.
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Carmona, P., Petit, F. & Yor, M. Some extensions of the arc sine law as partial consequences of the scaling property of Brownian motion. Probab. Th. Rel. Fields 100, 1–29 (1994). https://doi.org/10.1007/BF01204951
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DOI: https://doi.org/10.1007/BF01204951