A weak law of large numbers for realised covariation in a Hilbert space setting

A Note on the Strong Law of Large Numbers

Petrov (1996) proved the connection between general moment conditions and the applicability of the strong law of large numbers to a sequence of pairwise independent and identically distributed random variables. This note examines this connection to a sequence of pairwise negative quadrant dependent (NQD) and identically distributed random variables. As a consequence of the main theorem ...

Weak Law of Large Numbers + the AEP

An Exact Weak Law of Large Numbers

This paper explores a Weighted Exact Weak Law, where the classical Weak Law fails and the corresponding Strong Law also fails. This type of result comes from the Fair Games problem and is associated with the St Petersburg Game.

A Strong Law of Large Numbers for Aana Random Variables in a Hilbert Space and Its Application

In this paper we introduce the concept of asymptotically almost negatively associated random variables in a Hilbert space and obtain the strong law of large numbers for a strictly stationary asymptotically almost negatively associated sequence of H-valued random variables with zero means and finite second moments. As an application we prove a strong law of large numbers for a linear process gen...

A law of large numbers for fuzzy numbers in a Banach space

We study the following problem: If ξ1, ξ2, . . . are fuzzy numbers with modal values M1, M2, . . . , then what is the strongest t-norm for which lim n→∞ Nes ( mn − ≤ ξ1 + · · · + ξn n ≤ mn + ) = 1, for any > 0, where mn = M1 + · · · + Mn n , the arithmetic mean ξ1 + · · · + ξn n is defined via sup-t-norm convolution and Nes denotes necessity.