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The boundary dimension of B [0 , 1] is the Hausdorff dimension of the “frontier” of Brownian motion, where the frontier of planar Brownian motion is t he boundary of the un-
submitted March 20, 2000 Final version accepted April 14, 2000 AMS 1991 Subject classification: Primary 60J45; Secondary 60J65, 31C15 Brownian motion, capacity, polar set,
Key words: intersection local time, moderate deviations, planar, random walks, large de- viations, Brownian motion, Gagliardo-Nirenberg, law of the iterated logarithm.. AMS 2000
We prove that the Hausdorff dimension of the frontier equals 2(1 − α ) where α is an exponent for Brownian motion called the two-sided disconnection exponent.. In particular, using
As a consequence of Theorem 3.2, Corollary 3.3 and Lemma 3.4, the following result gives the Hausdorff dimension and packing dimension of the intersection of two independent
Keywords and phrases: Level crossings, fractional Brownian motion, limit theo- rem, local time, rate of convergence.. AMS subject classification (2000): Primary 60F05; Secondary
Key words: Exit place of Brownian motion, parabolic-type domain, horn-shaped domain, h - transform, Green function, harmonic measure.. AMS 2000 Subject Classification:
Key words: Martingale, differential subordination, orthogonal martingales, moment inequality, stochastic integral, Brownian motion, best constants.. AMS 2000 Subject
