The aim of the paper is to establish strong laws of large numbers for sequences of blockwise and pairwise -dependent random variables in a convex combination space with or without compactly uniformly integrable condition. Some of our results are even new in the case of real random variables.
A sequence of random elements is called strongly tight if for an arbitrary there exists a compact set such that . For the Polish space valued sequences of random elements we show that almost sure convergence of as well as weak convergence of randomly indexed sequence assure strong tightness of . For bounded Banach space valued asymptotic martingales strong tightness also turns out to the sufficient condition of convergence. A sequence of r.e. is said to converge essentially with...
Let be a stochastically continuous, separable, Gaussian process with . A sufficient condition, in terms of the monotone rearrangement of , is obtained for to have continuous sample paths almost surely. This result is applied to a wide class of random series of functions, in particular, to random Fourier series.
Si considera, sul gruppo degli interi, una passeggiata aleatoria uscente dall’origine, i cui passi ammettano due soli possibili valori: uno strettamente negativo, l’altro strettamente positivo. Nel caso particolare in cui il primo di questi valori sia , si dà un’espressione esplicita per la legge del primo istante di ritorno nell’origine.