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Pré-Publication, Document De Travail Année : 2019

Green's functions with oblique Neumann boundary conditions in a wedge

Résumé

We study semi-martingale obliquely reflected Brownian motion (SRBM) with drift in a wedge of the plane in the transient case. Our main result determines a general explicit integral expression for the Laplace transform of Green's functions of this process. To that purpose we establish a new kernel functional equation connecting Laplace transforms of Green's functions inside the wedge and on its edges. This is reminiscent of the recurrent case where a functional equation derives from the "Basic adjoint relationship" which characterizes the stationary distribution. This equation leads us to a non-homogeneous Carleman boundary value problem. Its resolution provides a formula for the Laplace transform function in terms of contour integrals and a conformal mapping.
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Dates et versions

hal-02123641 , version 1 (08-05-2019)
hal-02123641 , version 2 (24-09-2020)

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Sandro Franceschi. Green's functions with oblique Neumann boundary conditions in a wedge. 2019. ⟨hal-02123641v1⟩

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