Central Limit Theorem for Banach Space Valued Fuzzy Random Variables

Weak laws of large numbers for weighted sums of Banach space valued fuzzy random variables

In this paper, we present some results on weak laws of large numbers for weighted sums of fuzzy random variables taking values in the space of normal and upper-semicontinuous fuzzy sets with compact support in a separable real Banach space. First, we give weak laws of large numbers for weighted sums of strong-compactly uniformly integrable fuzzy random variables. Then, we consider the case that...

Strong laws of large numbers for independent fuzzy set-valued random variables

In this paper, we shall present strong laws of large numbers (SLLN’s) for independent (not necessary identically distributed) fuzzy set-valued random variables whose base space is a separable Banach space or an Euclidean space, in the sense of the extended Hausdorff metric d∞ H .We apply the method to the sequence of independent identically distributed fuzzy set-valued random variables to give ...

Central and Local Limit Theories in Markov Dependent Random Variables

The Clark–ocone Formula for Vector Valued Random Variables in Abstract Wiener Space

Erratum to " The Clark-Ocone formula for vector valued random variables in abstract Wiener space " , Jour. In this paper we considered the extension of the Clark-Ocone formula for a random variable defined on an abstract Wiener space (W, H, µ) and taking values in a Banach space (denoted there either B or Y). The main result appears in Theorem 3.4. Unfortunately, as first pointed out to us by J...

Central Limit Theorem for Truncated Heavy Tailed Ba- Nach Valued Random Vectors

Situations where heavy-tailed distributions is a good fit, and at the same time there is a physical upper bound on the quantity of interest, are common in nature. Clearly, the natural model for phenomena like this is a truncated heavy-tailed distribution a distribution that matches a heavytailed one till a specified limit and after that it decays significantly faster or simply vanishes. This le...