Iterated Logarithm Laws for Asymmetric Random Variables Barely with or Without Finite Mean

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.

Strong Laws for Weighted Sums of Negative Dependent Random Variables

In this paper, we discuss strong laws for weighted sums of pairwise negatively dependent random variables. The results on i.i.d case of Soo Hak Sung [9] are generalized and extended.

ON THE LAWS OF LARGE NUMBERS FOR DEPENDENT RANDOM VARIABLES

In this paper, we extend and generalize some recent results on the strong laws of large numbers (SLLN) for pairwise independent random variables [3]. No assumption is made concerning the existence of independence among the random variables (henceforth r.v.’s). Also Chandra’s result on Cesàro uniformly integrable r.v.’s is extended.

Chover-Type Laws of the Iterated Logarithm for Continuous Time Random Walks

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 ...