Asymptotic behavior of $p$-predictions for vector valued random variables

ASYMPTOTIC BEHAVIOR OF p-PREDICTIONS FOR VECTOR VALUED RANDOM VARIABLES

Let (Q,<r, p) be a probability space and let X be a B-valued /i-essentially bounded random variable, where (B,\\ ||) is a uniformly convex Banach space. Given a, a sub-<r-algebra of a, the p-prediction (1 < p < oo) of X is defined as the best Lp-approximation to X by (»-measurable random variables. The paper proves that the Pólya algorithm is successful, i.e. the p-prediction converges to an "c...

Asymptotic Behavior of Weighted Sums of Weakly Negative Dependent Random Variables

Let be a sequence of weakly negative dependent (denoted by, WND) random variables with common distribution function F and let be other sequence of positive random variables independent of and for some and for all . In this paper, we study the asymptotic behavior of the tail probabilities of the maximum, weighted sums, randomly weighted sums and randomly indexed weighted sums of heavy...

Asymptotic Fluctuation Behavior of Sums of Weakly Dependent Random Variables*

Asymptotic Expansions for the Laplace Approximations of Sums of Banach Space-valued Random Variables

Let Xi, i ∈ N, be i.i.d. B-valued random variables, where B is a real separable Banach space. Let Φ be a smooth enough mapping from B intoR. An asymptotic evaluation of Zn = E(exp(nΦ( ∑n i=1 Xi/n))), up to a factor (1 + o(1)), has been gotten in Bolthausen [Probab. Theory Related Fields 72 (1986) 305–318] and Kusuoka and Liang [Probab. Theory Related Fields 116 (2000) 221–238]. In this paper, a...

On Chung-Teicher type strong law for arrays of vector-valued random variables

We study the equivalence between the weak and strong laws of large numbers for arrays of row-wise independent random elements with values in a Banach space . The conditions under which this equivalence holds are of the Chung or Chung-Teicher types. These conditions are expressed in terms of convergence of specific series and o(1) requirements on specific weighted row-wise sums. Moreover, there ...