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Key words: Self-similar Markov process, L´evy process, Lamperti representation, last pas- sage time, time reversal, integral test, law of the iterated logarithm.. AMS 2000
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-
Keywords: Brownian motion with trend, boundary crossing probability, large deviations, exact
Keywords : fractional Brownian motion, function series expansion, rate of convergence, Gamma-mixed Ornstein–Uhlenbeck process.. AMS subject classification:
Keywords: Gaussian random walk; maximum; Riemann zeta function; Euler-Maclaurin summa- tion; equidistant sampling of Brownian motion; finite
Keywords Wiener space, Sobolev space, Stochastic integral, Fractional Brownian Motion, Itˆ o’s formula.. AMS Subject Classification (1991)
Our proof follows recent work by Denisov and Wachtel who used mar- tingale properties and a strong approximation of random walks by Brownian motion.. Therefore, we are able to
Key words: Weak convergence, Bernoulli random walks, Brownian meander, bridge, ex- cursion, peaks.... } be the set of
