Geodesic
Sharp estimates of the Green function of hyperbolic Brownian motion
Kamil Bogus 1   ; Tomasz Byczkowski 2   ; Jacek Małecki 1
1 Faculty of Pure and Applied Mathematics Wrocław University of Technology Wybrzeże Wyspiańskiego 27 50-370 Wrocław, Poland
2 Institute of Mathematics Polish Academy of Sciences Śniadeckich 8 00-656 Warszawa, Poland and Faculty of Pure and Applied Mathematics Wrocław University of Technology Wybrzeże Wyspiańskiego 27 50-370 Wrocław, Poland
Studia Mathematica, Tome 228 (2015) no. 3, pp. 197-221 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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The main objective of the work is to provide sharp two-sided estimates of the $\lambda $-Green function, $\lambda \geq 0$, of the hyperbolic Brownian motion of a half-space. We rely on the recent results obtained by K. Bogus and J. Małecki (2015), regarding precise estimates of the Bessel heat kernel for half-lines. We also substantially use the results of H. Matsumoto and M. Yor (2005) on distributions of exponential functionals of Brownian motion.
DOI : 10.4064/sm228-3-1
Keywords: main objective work provide sharp two sided estimates lambda green function lambda geq hyperbolic brownian motion half space rely recent results obtained bogus ecki regarding precise estimates bessel heat kernel half lines substantially results matsumoto yor distributions exponential functionals brownian motion

Kamil Bogus  1   ; Tomasz Byczkowski  2   ; Jacek Małecki  1

1 Faculty of Pure and Applied Mathematics Wrocław University of Technology Wybrzeże Wyspiańskiego 27 50-370 Wrocław, Poland
2 Institute of Mathematics Polish Academy of Sciences Śniadeckich 8 00-656 Warszawa, Poland and Faculty of Pure and Applied Mathematics Wrocław University of Technology Wybrzeże Wyspiańskiego 27 50-370 Wrocław, Poland 
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     title = {Sharp estimates of the {Green} function of
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Kamil Bogus; Tomasz Byczkowski; Jacek Małecki. Sharp estimates of the Green function of
 hyperbolic Brownian motion. Studia Mathematica, Tome 228 (2015) no. 3, pp. 197-221. doi: 10.4064/sm228-3-1

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