Abstract
We study the three-dimensional joint distribution of a Brownian motion and the integrals of its exponential and its exponential squared from some points of view. We show an explicit expression of the Laplace transform of the distribution, which gives an extension of Yor’s resutlt on the two-dimensional one. We apply the result to some problems, in particular, to the calculation of an explicit form of the heat kernel of the semigroup generated by the Maass Laplacian on the Poincaré upper half plane.
Larbi Alili: Partially supported by the Austrian Science Foundation (FWF) under grant Wittgenstein-Prize
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© 2001 Springer-Verlag Berlin/Heidelberg
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Alili, L., Matsumoto, H., Shiraishi, T. (2001). On a Triplet of Exponential Brownian Functionals. In: Azéma, J., Émery, M., Ledoux, M., Yor, M. (eds) Séminaire de Probabilités XXXV. Lecture Notes in Mathematics, vol 1755. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-44671-2_27
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DOI: https://doi.org/10.1007/978-3-540-44671-2_27
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