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

Sandro Franceschi; Irina Kourkova; Maxence Petit

doi:10.1007/s11134-024-09925-y

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arXiv · 2310.02673

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

Sandro Franceschi·Irina Kourkova·Maxence Petit

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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.

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Sandro Franceschi, Irina Kourkova, Maxence Petit. 2023-10-04. Asymptotics for the Green's functions of a transient reflected Brownian motion in a wedge. https://doi.org/10.1007/s11134-024-09925-y

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