Conformal restriction of Brownian excursion with darning.

Let 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 . Based on the existence of the two-sided restriction measure, we show that possesses conformal restriction property, extending the conformal restriction of the Brownian excursion for a simply connected domain. [ABSTRACT FROM AUTHOR]