Implementation and Analysis of Shared-Control Guidance Paradigms for Improved Robot-Mediated Training

In Esary et al.[16], association---a property of the covariance of random fields, was shown to be a natural generalization of independence.

In this work we concentrate on a new covariance-like function called Dep.

The first part of the paper concentrates on some basic relationships that Dep has with the most common mixing coefficients including two new central limit theorems.

I then work out a more rigorous treatment of the function, showing that it is closed under limits, etc.

Basic covariance properties that hold for associated random fields and quadrant dependent fields are examined using this function.

Natural extensions of the Hoeffding lemma and Rosenthal-like inequalities for mixing random variables like those given by Emmanuel Rio[23] are solved in terms of Dep.

Based on the work done by Newman[19][20][21], Cox[12], Bulinski[8] and others, a triangular array central limit theorem, utilizing Dep, is presented with applications to positively associated and negatively associated random fields.

The parabolic Anderson equation[11], a stochastic heat equation that models the flow of electrons through a crystaline lattice, is explored in detail.

Solutions to the parabolic Anderson equation are shown to be associated, and I discuss how to combine solutions of the discrete parabolic Anderson equation to converge to a Gaussian Field.