Strong ergodicity of monotone transition functions

By revealing close links among strong ergodicity, monotone, and the Feller–Reuter–Riley (FRR) transition functions, we prove that a monotone ergodic transition function is strongly ergodic if and only if it is not FRR. An easy to check criterion for a Feller minimal monotone chain to be strongly ergodic is then obtained. We further prove that a non-minimal ergodic monotone chain is always strongly ergodic. The applications of our results are illustrated using birth-and-death processes and branching processes.

Ergodicity and stability of generalised Markov branching processes with resurrection

This paper concentrates on investigating ergodicity and stability for generalised Markov branching processes with resurrection. Easy checking criteria including several clear-cut corollaries are established for ordinary and strong ergodicity of such processes. The equilibrium distribution is given in an elegant closed form for the ergodic case. The probabilistic interpretation of the results is clear and thus explained.

An integrated study (geochemistry, stable oxygen and carbon isotopes, nannofossils, planktonic foraminifera, inoceramid bivalves, ammonites and crinoids) of the Waxahachie Dam Spillway section, north Texas: a possible boundary stratotype for the base of the Campanian Stage

The spillway of Lake Waxahachie, Ellis County (Texas), exposes a > 17 m section of the Hutchins Member of the Austin Chalk Group, un-conformably overlain by Taylor Clay. The Austin sequence was regarded as a potential Global Stratotype Section for the base of the Campanian Stage at the 1995 Brussels meeting on Cretaceous Stage boundaries, with the last occurrence of the crinoid Marsupites testudinarius (von Schlotheim, 1820) as the potential boundary marker. An integrated study of the geochemistry, stable carbon and oxgen isotopes, nannofossils, planktonic foraminifera, inoceramid bivalves, ammonites and crinoids of this section place the last occurrence of M. testudinarius in a matrix of eighteen ancillary biostratigraphic markers, while the boundary can also be recognised on the basis of a delta C-13 excursion that can, in principle, be detected globally in marine sediments. A new forma of the crinoid Marsupites testudinarius is introduced. The Waxahachie section fulfils sufficient geological criteria as to be an excellent candidate GSSP for the base of the Campanian Stage, if problems of ownership and access to the section can be resolved.