Geodesic
On the distribution of inhomogeneous functionals of Brownian local time at the inverse local time moment
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 36, Tome 535 (2024), pp. 40-57 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider the question: how to calculate distributions of the simplest inhomogeneous integral functional of Brownian local time with respect to space parameter at the inverse local time moment. For the Laplace transform of distribution of such a functional we obtain formulas expressed in terms of solutions of the second order differential equations, satisfying some boundary conditions. As an application of these formulas the joint distribution of suprema of Brownian local time at adjacent intervals considered at the inverse local time moment are derived. 
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     title = {On the distribution of inhomogeneous functionals of {Brownian} local time at the inverse local time moment},
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A. N. Borodin. On the distribution of inhomogeneous functionals of Brownian local time at the inverse local time moment. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 36, Tome 535 (2024), pp. 40-57. http://geodesic.mathdoc.fr/item/ZNSL_2024_535_a3/

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