Asymptotics for the Green’s functions of a transient reflected Brownian motion in a wedge

Sandro Franceschi (), Irina Kourkova () and Maxence Petit ()
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Sandro Franceschi: Institut Polytechnique de Paris, Télécom SudParis, Laboratoire SAMOVAR
Irina Kourkova: Sorbonne Universite, Laboratoire de Probabilités, Statistiques et Modélisation, UMR 8001
Maxence Petit: Sorbonne Universite, Laboratoire de Probabilités, Statistiques et Modélisation, UMR 8001

Queueing Systems: Theory and Applications, 2024, vol. 108, issue 3, No 4, 382 pages

Abstract: Abstract We consider a transient Brownian motion reflected obliquely in a two-dimensional wedge. A precise asymptotic expansion of Green’s functions is found in all directions. To this end, we first determine a kernel functional equation connecting the Laplace transforms of the Green’s functions. We then extend the Laplace transforms analytically and study its singularities. We obtain the asymptotics applying the saddle point method to the inverse Laplace transform on the Riemann surface generated by the kernel.

Date: 2024
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DOI: 10.1007/s11134-024-09925-y

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