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.

Birth-death processes with an instantaneous reflection barrier

A new structure with the special property that an instantaneous reflection barrier is imposed on the ordinary birth-death processes is considered. An easy-checking criterion for the existence of such Markov processes is first obtained. The uniqueness criterion is then established. In the nonunique case, all the honest processes are explicitly constructed. Ergodicity properties for these processes are investigated. It is proved that honest processes are always ergodic without necessarily imposing any extra conditions. Equilibrium distributions for all these ergodic processes are established. Several examples are provided to illustrate our results.

Birth-death processes with disaster and instantaneous resurrection

A new structure with the special property that instantaneous resurrection and mass disaster are imposed on an ordinary birth-death process is considered. Under the condition that the underlying birth-death process is exit or bilateral, we are able to give easily checked existence criteria for such Markov processes. A very simple uniqueness criterion is also established. All honest processes are explicitly constructed. Ergodicity properties for these processes are investigated. Surprisingly, it can be proved that all the honest processes are not only recurrent but also ergodic without imposing any extra conditions. Equilibrium distributions are then established. Symmetry and reversibility of such processes are also investigated. Several examples are provided to illustrate our results.

Giving credit where it's due

Discusses the entitlement to occupation rent where one party to a relationship no longer lives in the matrimonial or family home in which he/she has an interest and a right of occupation. Describes the case law illustrating that forceful exclusion of the non-occupying party is not a prerequisite to entitlement to an occupation rent. Considers the calculation of the parties' respective credits where the occupying party has made mortgage repayments since the separation and the other is entitled to an occupation rent.

Meeting the emotional needs of parents who have a child with complex needs

The physical and financial demands of caring for a child with complex needs are acknowledged by health professionals. However, the emotional needs of parents are not often recognized by health professionals until parents are at a heightened level of stress. This paper is based on a literature review of current articles, research papers and government documentation. The focus is on the emotional impact to parents who have a child with complex needs, particularly at the point of diagnosis. The paper explores how health professionals, and nurses in particular, should meet the emotional needs of parents in order to support them more effectively. Giving birth to a child with severe health problems impacts upon parents at an emotional time of transition, particularly if there were no concerns identified during pregnancy. For some parents a grief response or state of chronic sorrow may be triggered. The reality of caring for a baby who is critically ill or disabled can be an enormous and unexpected shock for both parents. Parents need emotional support and guidance, as they may have to change their expectations for their child’s development and even life span. It is important for nurses to realise that if parents’ emotional needs are unmet it can lead to clinical depression or mental illness. Primary support often comes from parent support groups rather than health professionals. The review highlights factors affecting parents’ emotions and discusses how early support, home visits and practical help can all help to alleviate parents’ emotional stress.

Meeting the emotional needs of parents who have a child with complex needs

The physical and financial demands of caring for a child with complex needs are acknowledged by health professionals. However the emotional needs of parents are not often recognised by health professionals until parents are at a heightened level of stress. This paper is based on a literature review of current articles, research papers and government documentation. The focus is on how health professionals, and nurses in particular should meet the emotional needs of parents who have child with complex needs, particularly at the point of diagnosis. Giving birth to a child with severe health problems impacts upon parents at an emotional time of transition, particularly if there were no concerns identified during pregnancy. For some parents a grief response or state of chronic sorrow may be triggered. The reality of caring for a baby who is critically ill or disabled can be an enormous and unexpected shock for both parents. Parents need emotional support and guidance, as they may have to change their expectations for their child’s development and even life span. Primary support often comes from parent support groups rather than health professionals. The review discusses how home visits, practical help and early support can all help to alleviate stress. It is important for nurses to realise that if parents’ emotional needs are unmet they can lead to clinical depression or mental illness. This literature review looks at the emotional impact on parents and explores how nurses can address this issue in order to support parents more effectively. It identifies key areas that nurses could address that would help alleviate parents’ emotional stress.

Grandparents and parenting: towards a theory of grandparenthood

This paper explores the changing role of contemporary grandparents with many demonstrating a willingness and ability to take on parental responsibilities for their grandchildren, where they may face challenges and opportunities in difficult times. Three main forms of grand parenting are identified in the literature, those who have primary responsibility and are raising their grand children as their main carers perhaps in response to crisis situations, those who live in extended families and participate in care, and those who provide day care while the child’s parents work. The latter has increased because of the increasing frequency of divorce, single parenting and the lack of available or subsidised child care in the United Kingdom. When grandparents step into a troubled situation and attempt to offer stability and security for their grandchildren they may have to manage the combined responsibilities of family caregivers and parental figures. Grandparenthood is a tenuous role, lacking clear agreement on behaviour norms. In the culture of advice and parenting support, while care must be taken not to undermine parenting skills or make judgements about the ability to cope with the demands of childcare, an exploration of the impact on grandparents and children must be undertaken. Due to the complex web of interrelated factors the process and outcomes of care giving by grandparents is not well known in the literature. It is proposed therefore that it is timely for research to be undertaken to explore and develop a theory of Grandparenthood.