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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-
By Skorokhod embedding of mean zero, finite variance random variables in Brownian motion, there is a stopping time τ such that for any standard Brownian motion (i.e., starting
The radial projection of a Brownian motion started at the origin and run for unit time in d dimensions defines a random occupation measure on the sphere S d− 1.. Can we determine
Keywords Brownian bridge, Brownian excursion, Brownian scaling, local time, Bessel process, zeros of Bessel functions, Riemann zeta function.. AMS subject classification 60J65,
the time reversed process is a drifted fractional Brownian motion, which continuously extends the one obtained in the theory of time reversal of Brownian diffusions when H = 1/2..
The expression just obtained for the distribution of coalescing Brownian motions is closely related to the formula for the transition density of the interlaced Brownian motions given
This process has values which are trajectories of standard Poisson process stopped at some random finite lifetime with Brownian evolution.. We use this Poisson snake to construct
A closed formula for the mean of a maximum likelihood estimator associated with the Brownian bridge is obtained; the exact relation with that of the Brownian motion is
