A limit theory is developed for the least squares estimator for mildly and purely explosive autoregressions under drifting sequences of parameters with autoregressive roots ρn satisfying ρn Ç ρ ∈ (-É, -1] ∪ [1, É) and n (

It is proved that infinitesimal triangular arrays obtained from normalized partial sums of strongly mixing (but not necessarily stationary) random sequences can produce as limits only selfdecomposable distributions.

In this paper, we state several convergence results with respect to the Mosco topology of strong laws of large numbers for triangular arrays of rowwise independent random sets in a separable Banach space of type p(1<p≤2). We also provide some typical examples illustrating this study.