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.
In this paper we are concerned with the norm almost sure convergence of series of random vectors taking values in some linear metric spaces and strong laws of large numbers for sequences of such random vectors. Section 2 treats the Banach space case where the results depend upon the geometry of the unit cell. Section 3 deals with spaces equipped with a non-necessarily homogeneous -norm and in Section 4 we restrict our attention to sequences of identically distributed random vectors.
In this paper we get some results about the asymptotic behaviour of the sequenceΠn = 1 + X1 + X1X2 + X1X2X3 + ...where {Xn}n=1∞ are i.i.d. random variables. Strong limit laws, Central limit theorem and Iterated Logarithm law are obtained, after an analysis of the convergence of Πn. Rates of convergence are also given.
* Research supported by NATO GRANT CRG 900 798 and by Humboldt Award for U.S. Scientists.In this paper a general theory of a random number of random variables is constructed. A description of all random variables ν admitting an analog of the Gaussian distribution under ν-summation, that is, the summation of a random number ν of random terms, is given. The v-infinitely divisible distributions are described for these ν-summations and finite estimates of the approximation of ν-sum distributions with...
We consider S-unimodal Misiurewicz maps T with a flat critical point c and show that they exhibit ergodic properties analogous to those of interval maps with indifferent fixed (or periodic) points. Specifically, there is a conservative ergodic absolutely continuous σ-finite invariant measure μ, exact up to finite rotations, and in the infinite measure case the system is pointwise dual ergodic with many uniform and Darling-Kac sets. Determining the order of return distributions to suitable reference...
The problem of finding simple additional conditions, for a weakly convergent sequence in , which would suffice to imply strong convergence has been widely studied in recent years. In this Note we study this problem for Banach valued random vectors, by replacing weak convergence with a less restrictive assumption. Moreover, all the additional conditions we consider are also necessary for strong convergence, and they depend only on marginal distributions.
Soit la rotation sur le cercle d’angle irrationnel , soit une marche aléatoire transiente sur . Soit et , nous étudions la convergence faible de la suite