Law-Invariant Functionals on General Spaces of Random Variables

A Note on Invariant Random Variables

One method of improving safety of transmissions between simple sensing devices is to assign sets of cryptographic keys to them. Methods of distributions of such keys are called key predistribution schema. The basic probabilistic key predistribution schema from Eschenauer and Gligor (2002) can be described as follows: we have a pool K of cryptographic symmetric keys of cardinality n; each device...

On the Convergence Rate of the Law of Large Numbers for Sums of Dependent Random Variables

In this paper, we generalize some results of Chandra and Goswami [4] for pairwise negatively dependent random variables (henceforth r.v.’s). Furthermore, we give Baum and Katz’s [1] type results on estimate for the rate of convergence in these laws.

Sample Spaces, Random Variables

1 Probabilities In talking about probabilities, the fundamental object is Ω, the sample space. Points (elements) in Ω are denoted (generically) by ω. We assign probabilities to subsets of Ω. Assume for the moment that Ω is finite or countably infinite. Thus Ω could be the space of all possible outcomes when a coin is tossed three times in a row or say, the set of positive integers. A probabilit...

On a Metric on Translation Invariant Spaces

In this paper we de ne a metric on the collection of all translation invarinat spaces on a locally compact abelian group and we study some properties of the metric space.

A Representation for Characteristic Functionals of Stable Random Measures with Values in Sazonov Spaces