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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2310.02673 |
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| _version_ | 1866912048161488896 |
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| author | Franceschi, Sandro Kourkova, Irina Petit, Maxence |
| author_facet | Franceschi, Sandro Kourkova, Irina Petit, Maxence |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_02673 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Asymptotics for the Green's functions of a transient reflected Brownian motion in a wedge Franceschi, Sandro Kourkova, Irina Petit, Maxence Probability 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. |
| title | Asymptotics for the Green's functions of a transient reflected Brownian motion in a wedge |
| topic | Probability |
| url | https://arxiv.org/abs/2310.02673 |