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| Main Author: | |
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| Format: | Preprint |
| Published: |
2019
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1905.04049 |
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Table of Contents:
- We study semi-martingale obliquely reflected Brownian motion with drift in the first quadrant of the plane in the transient case. Our main result determines a general explicit integral expression for the moment generating function of Green's functions of this process. To that purpose we establish a new kernel functional equation connecting moment generating functions of Green's functions inside the quadrant 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 moment generating function in terms of contour integrals and a conformal mapping.