We consider independent random variables {Xn} with a common distribution function F in the domain of attraction of an asymmetric stable law with exponent α≠1, and we prove limit infimum results for subsequences of partial sums of Xn and random sums.

A least squares estimation approach for the estimation of a GARCH (1,1) modelis developed. The asymptotic properties of the estimator are studied given mild regularity conditions, which require only that the error term has a conditionalmomen t of some order. We establish the consistency,...

We consider a nearest neighbor random walk on Z which is reflecting at 0 and perturbed when it reaches its maximum. We compute the law of the hitting times and derive many corollaries, especially invariance principles with (rather) explicit descriptions of the asymptotic laws. We also obtain...