A Fluctuation Theorem for Cyclic Random Variables

A fluctuation theorem in a random environment

The space of the random events Ω will be supposed a space of sequences of finitely many symbols ω = {ωj}j=−∞, for instance a sequence of spins ωj = ±1, with the usual metric d(ω,ω) = ∑ j |ωj − ω j|2, and with τ the shift to the left: (τω)j = ωj+1. A “reflection” operation will be defined on Ω as ω←→ωT , with (ω )j = ω−j. The probability distribution P will be a τ–invariant and reflection–invari...

A decomposition theorem for fuzzy set-valued random variables

In this paper, a decomposition theorem for a (square integrable) fuzzy random variable FRV is proposed. The paper is mainly divided in two parts. In the first part, for any FRV X, we define the Hukuhara set as the family of (deterministic) fuzzy sets C for which the Hukuhara difference X ⊖H C exists almost surely; in particular, we prove that such a family is a closed (with respect to different...

A Local Limit Theorem for Sums of Dependent Random Variables

A version of central limit is established normalized sums dependent random when a theorem is and conditional are sufficiently The proof ideas from by representing density as integral of score function a translation of distributions. 1980 Subject 60F99.

Bell ’ s Theorem and Random Variables

Bell’s theorem states that quantum correlation function of two spins can not be represented as an expectation value of two classical random variables. Spin is described in Bell’s model by a single scalar random variable. We discuss another classical model of spin in which spin is described by a triple of classical random variables. It is shown that in this model the quantum correlation function...

Dominated Convergence for Fuzzy Random Variables