Conformal restriction of Brownian excursion with darning. (English) Zbl 1420.60092
Summary: Let \( E^\ast_t \) be a two-dimensional Brownian excursion with darning on a finitely connected domain. Using Koebe’s theorem and conformal invariance of Brownian motion with darning we derive that a two-sided restriction measure exists for \( E^\ast_t \). Based on the existence of the two-sided restriction measure, we show that \( E^\ast_t \) possesses conformal restriction property, extending the conformal restriction of the Brownian excursion for a simply connected domain.
MSC:
| 60H30 | Applications of stochastic analysis (to PDEs, etc.) |
| 60J65 | Brownian motion |
| 30C20 | Conformal mappings of special domains |
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