Burdzy, KrzysztofToby, Ellen H.Williams, Ruth J.2005-12-092005-12-091989Burdzy, K. , E.H. Toby, & R.J. Williams (1989). On Brownian excursions in Lipschitz domains. Part II: Local asymptotic distributions. In Seminar on Stochastic Processes 1988, eds. J. Glover, E. Çinlar, K. L. Chung & R. K. Getoor. Boston: Birkhäuser Boston, Inc., 55-85.http://hdl.handle.net/1773/2248In this paper, we continue the study initiated in Burdzy and Williams (1986) of the local properties of Brownian excursions in Lipschitz domains. The focus in part I was on local path properties of such excursions. In particular, a necessary and sufficient condition was given for Brownian excursions in a Lipschitz domain to share the local path properties with Brownian excursions in a half-space. This condition holds for C [to the power of 1, alpha] -domains ([alpha] > 0), but there is a C [to the power of 1]-domain for which it fails. Here we consider the distributions of a selection of local events for excursions. In particular, we focus on the asymptotics of these distributions as the region of locality shrinks to a point. We show that when a Lipschitz domain is locally approximated by a half-space, the asymptotics for excursions in the two domains are comparable.243038 bytesapplication/pdfen-USBrownian motionLipschitz domainslocal path propertiesBrownian excursionsBook chapter