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| Natura: | Preprint |
| Pubblicazione: |
2019
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/1905.04049 |
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| _version_ | 1866913670053756928 |
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| author | Franceschi, Sandro |
| author_facet | Franceschi, Sandro |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1905_04049 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Green's Functions with Oblique Neumann Boundary Conditions in the Quadrant Franceschi, Sandro Probability 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. |
| title | Green's Functions with Oblique Neumann Boundary Conditions in the Quadrant |
| topic | Probability |
| url | https://arxiv.org/abs/1905.04049 |