Birth-death processes with mass annihilation and state-dependent immigration

A birth-death process is subject to mass annihilation at rate β with subsequent mass immigration occurring into state j at rateα j . This structure enables the process to jump from one sector of state space to another one (via state 0) with transition rate independent of population size. First, we highlight the difficulties encountered when using standard techniques to construct both time-dependent and equilibrium probabilities. Then we show how to overcome such analytic difficulties by means of a tool developed in Chen and Renshaw (1990, 1993b); this approach is applicable to many processes whose underlying generator on E\{0} has known probability structure. Here we demonstrate the technique through application to the linear birth-death generator on which is superimposed an annihilation/immigration process.

Existence, recurrence and equilibrium properties of Markov branching processes with instantaneous immigration

Attention has recently focussed on stochastic population processes that can undergo total annihilation followed by immigration into state j at rate αj. The investigation of such models, called Markov branching processes with instantaneous immigration (MBPII), involves the study of existence and recurrence properties. However, results developed to date are generally opaque, and so the primary motivation of this paper is to construct conditions that are far easier to apply in practice. These turn out to be identical to the conditions for positive recurrence, which are very easy to check. We obtain, as a consequence, the surprising result that any MBPII that exists is ergodic, and so must possess an equilibrium distribution. These results are then extended to more general MBPII, and we show how to construct the associated equilibrium distributions.

Distress in children with learning disabilities at a respite unit: perspective on their experiences

Numerous studies have investigated the benefits of respite to families with a disabled child. Far fewer have examined the effects on the child and none have systematically compared information about this from different sources. Reports of behavioural reactions and views on distress were gathered from parents, teachers and respite staff. Children were also asked for their views. Over half the children (54%) were reported to show medium or strong negative reactions lasting for 1 or more days by a parent or teacher. Reported reactions varied widely between home and school and no concordance was found between parents, teachers and respite staff groups regarding distress. Some children's views differed from those of their parent or teacher. The findings highlight the extent of differences in perspectives and suggest the need for greater awareness of the possible distress to children attending respite. This is discussed in relation to factors such as the potential conflict of interests between parents and children, communication and behavioural difficulties, and the context in which the child is observed.

Coping, conversation tactics and marital interaction in persons with acquired profound hearing loss (APHL): correlates of distress

This study investigated coping strategies, conversation tactics, and marital interaction in acquired profound hearing loss (APHL) and compared emotionally stable (n = 15) and emotionally distressed (n = 7) participants. Nominated family members were assessed on most measures. Comparisons were also made in the subgroup of married participants. A combined distress criterion was derived from scores on standardized measures of anxiety, depression, hearing handicap, and post-traumatic stress. Groups were compared on the Ways-of-Coping Checklist, a newly devised measure of conversation tactics, and on the Couple Behaviour Report. It was found that distressed APHL participants were more likely to cope through avoidance, self-blame, and wishful thinking, and they used more avoidant tactics in conversation. The coping profile of family members did not differentiate distress groups. However, there was some indication of greater employment of coercive tactics by family members of distressed participants. The results are consistent with the view that the coping style of a person with APHL and the nature of their conversational interactions with family members contribute to their level of distress. Implications for audiological rehabilitation are discussed.