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Distribution of functionals of Brownian motion stopped at a time that is inverse to local time

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Abstract

Integral functionals of Brownian motion and of Brownian local time, as well as the supremum of Brownian motion and the supremum of Brownian local time are considered. The obtained results allow the computation of the distributions of these functionals for a Brownian motion stopped at the moment when the local time attains first a given value at one of two levels. It has been established that for this stopping time the Brownian local time is a Markov process with respect to the space variable and the generating operator of the process has been found. Examples of the computation of the distributions of certain functionals are given.

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Authors
  1. A. N. Borodin
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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 184, pp. 37–61, 1990.

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Borodin, A.N. Distribution of functionals of Brownian motion stopped at a time that is inverse to local time. J Math Sci 68, 419–437 (1994). https://doi.org/10.1007/BF01254267

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  • DOI: https://doi.org/10.1007/BF01254267

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