Further results on the relationship between mu-invariant measures and quasi-stationary distributions for absorbing continuous-time Markov chains

This note considers continuous-time Markov chains whose state space consists of an irreducible class, C, and an absorbing state which is accessible from C. The purpose is to provide results on mu-invariant and mu-subinvariant measures where absorption occurs with probability less than one. In particular, the well-known premise that the mu-invariant measure, m, for the transition rates be finite is replaced by the more natural premise that m be finite with respect to the absorption probabilities. The relationship between mu-invariant measures and quasi-stationary distributions is discussed. (C) 2000 Elsevier Science Ltd. All rights reserved.

The effect of arousals during sleep onset on estimates of sleep onset latency

It is well established that insomniacs overestimate sleep-onset latency. Furthermore, there is evidence that brief arousals from sleep may occur more frequently in insomnia. This study examined the hypothesis that brief arousals from sleep influence the perception of sleep-onset latency. An average of four sleep onsets was obtained from each of 20 normal subjects on each of two nonconsecutive, counterbalanced, experimental nights. The experimental nights consisted of a control night (control condition) and a condition in which a moderate respiratory load was applied to increase the frequency of microarousals during sleep onset (mask condition). Subjective estimation of sleep-onset latency and indices of sleep quality were assessed by self-report inventory. Objective measures of sleep-onset latency and microarousals were assessed using polysomnography. Results showed that sleep-onset latency estimates were longer in the mask condition than in the control condition, an effect not reflected in objective sleep-stage scoring of sleep-onset latency. Furthermore, an increase in the frequency of brief arousals from sleep was detected in the mask condition, and this is a possible source for the sleep-onset latency increase perceived by the subjects. Findings are consistent with the concept of a physiological basis for sleep misperception in insomnia.