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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
Keywords: Key words: Lipschitz domains, Neumann problem, reflecting Brownian motion, mixed boundary problem, Skorokhod equation, weak uniqueness, uniqueness in law,
In the paper [STW], it was shown that “a Brownian motion reflected on an independent time-reversed Brownian motion is again a Brownian motion” combining the fact that the
In the second example, although the family of conditioned laws are tight in the Martin topology, they possess multiple limit points so that weak convergence fails altogether..
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)
Keywords: time-change, inverse subordinator, Gaussian process, Fokker–Planck equation, Kol- mogorov equation, fractional Brownian motion, time-dependent Hurst parameter, Volterra
This result has consequences for the Hausdorff dimension of the frontier of planar Brownian motion, and also for the Hausdorff dimension of the set of cut-points of planar
