It is shown that sequences of generalized semi-Markov processes converge in the sense of weak convergence of random functions if associated sequences of defining elements (initial distributions, transition functions and clock time distributions) converge. This continuity or stability is used to obtain information about invariant probability measures. It is shown that there exists an invariant p...

The theme of providing predictable criteria for absolute continuity and for mutual singularity of two density processes on a ltered probability space is extensively studied, e.g., in the monograph by J. Jacod and A. N. Shiryaev [JS]. While the issue of absolute continuity is settled there in full generality, for the issue of mutual singularity one technical di culty remained open ([JS], p210): ...

Coherent, convex and monetary risk measures were introduced in a setup where uncertain outcomes are modelled by bounded random variables. In this paper, we study such risk measures on maximal subspaces of Orlicz classes. This includes coherent, convex, and monetary risk measures on L-spaces for 1 ≤ p < ∞ and covers a wide range of interesting examples. Moreover, it allows for an elegant duality...

A sequence of elements an of R d converges to a limit a if and only if, for each ǫ > 0, the sequence an eventually lies within a ball of radius ǫ centered at a. It’s okay if the first few (or few million) terms lie outside that ball— and the number of terms that do lie outside the ball may depend on how big ǫ is (if ǫ is small enough it typically will take millions of terms before the remaining...

Effects of exercise on dynamic aspects of sleep have not been studied. We hypothesized exercise altered dynamic sleep morphology differently for healthy controls relative to chronic fatigue syndrome (CFS) patients. Sixteen controls (38 ± 9 years) and 17 CFS patients (41 ± 8 years) underwent polysomnography on baseline nights and nights after maximal exercise testing. We calculated transition pr...