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
| Identifer | oai:union.ndltd.org:ORGSU/oai:ir.library.oregonstate.edu:1957/16230 |
| Date | 28 January 1988 |
| Creators | Franzosa, Marie M. |
| Contributors | Burton Jr, Robert M. |
| Source Sets | Oregon State University |
| Language | en_US |
| Detected Language | English |
| Type | Thesis/Dissertation |
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