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It has been shown that certain types of random walks in random potentials and Brownian motion in Poissonian potentials undergo a phase transition from sub-ballistic to ballistic
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
Keywords: Gaussian random walk; maximum; Riemann zeta function; Euler-Maclaurin summa- tion; equidistant sampling of Brownian motion; finite
Keywords and phrases: Capacity on Wiener space, quasi-sure analysis, Ornstein–Uhlenbeck process, Brownian
Keywords Wiener space, Sobolev space, Stochastic integral, Fractional Brownian Motion, Itˆ o’s formula.. AMS Subject Classification (1991)
We use excursion theory and the ergodic theorem to present an extreme-value analysis of the classical law of the iterated logarithm (LIL) for Brownian
Keywords: time-change, inverse subordinator, Gaussian process, Fokker–Planck equation, Kol- mogorov equation, fractional Brownian motion, time-dependent Hurst parameter, Volterra
Key words: Weak convergence, Bernoulli random walks, Brownian meander, bridge, ex- cursion, peaks.... } be the set of
