A Strong Law of Large Numbers for Random Sets in Fuzzy Banach Space

MARCINKIEWICZ-TYPE STRONG LAW OF LARGE NUMBERS FOR DOUBLE ARRAYS OF NEGATIVELY DEPENDENT RANDOM VARIABLES

In the following work we present a proof for the strong law of large numbers for pairwise negatively dependent random variables which relaxes the usual assumption of pairwise independence. Let be a double sequence of pairwise negatively dependent random variables. If for all non-negative real numbers t and , for 1 < p < 2, then we prove that (1). In addition, it also converges to 0 in ....

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.

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 ...

A Note on Strong Laws of Large Numbers for Dependent Random Sets and Fuzzy Random Sets

marcinkiewicz-type strong law of large numbers for double arrays of negatively dependent random variables

in the following work we present a proof for the strong law of large numbers for pairwise negatively dependent random variables which relaxes the usual assumption of pairwise independence. let be a double sequence of pairwise negatively dependent random variables. if for all non-negative real numbers t and , for 1 < p < 2, then we prove that (1). in addition, it also converges to 0 in . the res...