Banuelos, RodrigoBass, Richard F.Burdzy, Krzysztof2005-11-182005-11-181990Bañeulos, R., R.F. Bass, & K. Burdzy. (1990). A representation of local time for Lipschitz surfaces. Probability Theory and Related Fields, 84, 521-547.http://hdl.handle.net/1773/2166Suppose that D [is an element of the set of Real numbers to the power of n], n [is greater than or equal to] 2, is a Lipschitz domain and let N[subscript]t(r) be the number of excursions of Brownian motion inside D with diameter greater than r which started before time t. Then rN[subscript]t(r) converges as r --> 0 to a constant multiple of local time on [partial derivative]D, a.s. and in L[to the power of]p for all p < infinity. The limit need not exist or may be trivial (0 or 1) in Hölder domains, non-tangentially accessible domains and domains whose boundaries have finite surface area.259960 bytesapplication/pdfenBrownian motionLipschitz surfacesLocal timeHölder domainsArticle