Laws of the Iterated Logarithm for Intersections of RandomWalks on Z

Laws of the Iterated Logarithm for Triple Intersections of RandomWalks on Z

Moderate deviations and laws of the iterated logarithm for the volume of the intersections of Wiener sausages

Using the high moment method and the Feynman-Kac semigroup technique, we obtain moderate deviations and laws of the iterated logarithm for the volume of the intersections of two and three dimensional Wiener sausages.

Laws of the Iterated Logarithm for Triple Intersections of Three Dimensional Random Walks

Let X = {Xn, n ≥ 1}, X ′ = {X ′ n, n ≥ 1} and X ′′ = {X ′′ n, n ≥ 1} be three independent copies of a symmetric random walk in Z3 with E(|X1| log+ |X1|) < ∞. In this paper we study the asymptotics of In, the number of triple intersections up to step n of the paths of X , X ′ and X ′′ as n→∞. Our main result is lim sup n→∞ In log(n) log3(n) = 1 π|Q| a.s. where Q denotes the covariance matrix of ...

Laws of the Iterated Logarithm for Symmetric Jump Processes

Based on two-sided heat kernel estimates for a class of symmetric jump processes on metric measure spaces, the laws of the iterated logarithm (LILs) for sample paths, local times and ranges are established. In particular, the LILs are obtained for β-stable-like processes on α-sets with β > 0.

Self-normalized laws of the iterated logarithm

Stronger versions of laws of the iterated logarithm for self-normalized sums of i.i.d. random variables are proved.