No description available.

Inaug.-diss.--Göttigen.

Inaug.-diss.--Göttigen.

Product densities have been widely used in the literature to give a concrete description of the distribution of a point process. A rigorous description of properties of product densities is presented with examples to show that in some sense these results are the best possible. Product densities are then used to discuss positive dependence properties of point processes. There are many ways of describing positive dependence. Two well known notions for Bernoulli random variables are the strong FKG inequalities and association, the strong FKG inequalities being much stronger. It is known, for example, from van den Berg and Burton, that the strong FKG inequalities are equivalent to all conditional distributions being associated, which is equivalent to all conditional distributions being positively correlated. In the case of point processes for which product densities exist, analogs of such positive dependence properties are given. Examples are presented to show that unlike the Bernoulli case none of these conditions are equivalent, although some are shown to be implied by others. / Graduation date: 1988

No description available.

Thesis (Ph. D.)--Oregon State University, 1988. / Typescript (photocopy). Includes bibliographical references (leaves 71-74). Also available on the World Wide Web.

Thesis--Universität Bern.

Thesis (Ph. D.)--Rutgers University, 2010. / "Graduate Program in Statistics and Biostatistics." Includes bibliographical references (p. 55-57).

Thesis (M.S.)--Brigham Young University. Dept. of Statistics, 2007. / Includes bibliographical references (p. 57-60).

<p> We study two objects: an ideal of a Hecke algebra, and a pairing in Galois cohomology.</p> <p> Let h be the Hecke algebra of cusp forms of weight 2, level n, and a fixed Dirichlet character modulo n generated by all Hecke operators, where n is an odd prime p or a product of two distinct odd primes N and p. We study the Eisenstein I ideal of h. We wrote a computer program to test whether Up - 1 generates this ideal, where Up is the pth Hecke operator in h. We found many cases of n and the character so that Up - 1 alone generates I. On the other hand, we found one example with N = 3 and p = 331 where Up - 1 does not generate I.</p> <p> Let K = Q(μn) be the nth cyclotomic field. Let S be the set of primes above p in K, and let G_K,S be the Galois group of the maximal extension of K unramified outside S. We study a pairing on cyclotomic p-units that arises from the cup product on H1(G_K,S, μp). This pairing takes values in a Gal(K/Q)-eigenspace of the p-part of the class group of K. Sharifi has conjectured that this pairing is surjective. We studied this pairing in detail by imposing linear relations on the possible pairing values. We discovered many values of n and the character such that these relations single out a unique nontrivial possibility for the pairing, up to a possibly zero scalar.</p> <p> Sharifi showed in [S2] that, under an assumption on Bernoulli numbers, the element Up - 1 generates the Eisenstein ideal I if and only if pairing with the single element p is surjective. In particular, in the instances for which we found a unique nontrivial possibility for the pairing, then if Up - 1 generates I, we know that the scalar up to which it is determined cannot be zero.</p> / Thesis / Master of Science (MSc)