Occupancy distributions in Markov chains via Doeblin's ergodicity coefficient

We apply Doeblin's ergodicity coefficient as a computational tool to approximate the occupancy distribution of a set of states in a homogeneous but possibly non-stationary finite Markov chain. Our approximation is based on new properties satisfied by this coefficient, which allow us to approximate a chain of duration n by independent and short-lived realizations of an auxiliary homogeneous Markov chain of duration of order ln(n). Our approximation may be particularly useful when exact calculations via first-step methods or transfer matrices are impractical, and asymptotic approximations may not be yet reliable. Our findings may find applications to pattern problems in Markovian and non-Markovian sequences that are treatable via embedding techniques.Comment: 12 pages, 2 table

Schools Respond to Risk Management Programs for Asbestos, Lead in Drinking Water and Radon

Based on a study of the three EPA-initiated, public school risk management programs noted in the title, the authors find that state agency involvement is an important factor in the success of such programs. They also find, e.g., that school districts are justifiably reluctant to comply with tentative program

Independent Partitions in Boolean Algebras

This dissertation introduces a generalization of the cardinal invariant independence for Boolean algebras, suggested by the proof of the Balcar-Franek Theorem. The objects of study are independent sets of partitions under this new notion of independence. Generalizations of several known results regarding large and small independence are formulated and proved, and counterexamples provided for others. Notably the Balcar-Franek theorem itself is generalized