We find necessary and sufficient conditions for the almost sure finiteness of weighted integrals of stable processes with parameters [alpha] = 1 and [beta] [not equal to] 0.

Let {Xn, n [greater-or-equal, slanted] 1} be a stationary [rho]-mixing sequence of random variables with EX1 = , EX12+[delta] for some and Var Sn --> [infinity] as n --> [infinity]. This note presents a class of estimators of Var Sn, without assuming any mixing rate.

In statistical analyses the complexity of a chosen model is often related to the size of available data. One important question is whether the asymptotic distribution of the parameter estimates normally derived by taking the sample size to infinity for a fixed number of parameters would remain...

Let W(t) be a standard Wiener process with local time L(x, t). It is well-known that, as stochastic processes, L(0, t) and supo [less-than-or-equals, slant] s [less-than-or-equals, slant] tW(s) have the same distribution (Lévy, 1939). Here we give a new derivation of the distribution of L(x, t...

In this note we estimate the convergence rate of strong law for [alpha]-mixing sequences under the nearly best possible condition on the mixing rate.

We give here an almost sure central limit theorem for associated sequences, strongly mixing and p-mixing sequences under the same conditions that assure that the central limit theorem holds.