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.

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.

Managing the risk of parenting

The aim of parents is to enable their children to become autonomous individuals capable of participating fully in the culture in which they live (Korbin 1997). Furthermore, the quality of parenting is reflected in an adult’s ability to recognize and adequately meet a child’s needs in a developmentally and emotionally appropriate manner (Donald & Jureidini 2004).Within contemporary society however, parents are faced with the tensions of providing boundaries whilst affording children rights. This in itself brings risks and a common thread that runs through approaches to parenting is the attempt to define a threshold of acceptable parenting. Above the threshold and a parent is good enough and below is not good enough. This paper will consider what the minimum requirements are and explore different dimensions of parenting. The concept of good enough parenting will be revisited in relation to risks that parents have to take, within the context of contemporary policy related to improving outcomes for children as enshrined in the Every Child Matters: Change for Children Agendas (Department for Education and skills 2003). The current dominance of a risk management approach to safeguarding children will be addressed within the context of a ‘risk society’ and the importance of the safety and well-being of the child will be examined It will be suggested that we need to achieve a better balance of ensuring the safety of the child, meeting the child's developmental needs, and supporting family functioning if we are to help parents manage the risks.

Spank performance tour [at National Review of Live Art 2008]

Spank is a duet about two women’s journeys as they play out different roles. One woman recalls stinging anecdotes marked by intimacy, jealousy, fear and fantasy from her childhood in the 70s suburbs – round the corner from where Mike Leigh would film Life Is Sweet. Her Double (projected on screen) reads from a newspaper about an event that punctured the local community, creating an enduring cultural scar, her voice lacking emotion. Both women must eventually face one another and ask, who is deceiving whom? The consequences of guilt and shame and the unstable shift from private memory to public consequence is inevitable and deadly.[ABSTRACT BY THE AUTHOR]