Stochastic monotonicity and duality for continuous time Markov chains with general q-Matrix

The key problems in discussing stochastic monotonicity and duality for continuous time Markov chains are to give the criteria for existence and uniqueness and to construct the associated monotone processes in terms of their infinitesimal q -matrices. In their recent paper, Chen and Zhang [6] discussed these problems under the condition that the given q-matrix Q is conservative. The aim of this paper is to generalize their results to a more general case, i.e., the given q-matrix Q is not necessarily conservative. New problems arise 'in removing the conservative assumption. The existence and uniqueness criteria for this general case are given in this paper. Another important problem, the construction of all stochastically monotone Q-processes, is also considered.

Existence, uniqueness and constructions for stochastically monotone Q-processes

The key problems in discussing duality and monotonicity for continuous-time Markov chains are to find conditions for existence and uniqueness and then to construct corresponding processes in terms of infinitesimal characteristics, i.e., q-matrices. Such problems are solved in this paper under the assumption that the given q-matrix is conservative. Some general properties of stochastically monotone Q-process ( Q is not necessarily conservative) are also discussed.

Characteristics and trends of self-harming behaviours in young people

Deliberate self-harm is recognized as a serious public health issue in young people. There is evidence that young people who self-harm are more likely to repeat self-harm, and this in turn increases their risk of completed suicide. Prevalence studies have identified that the rate of self-harm among young people is on the increase, information largely based on data arising from review and analysis of hospital attendances. However, community-based studies indicate that the prevalence is much higher, with those seen in emergency departments representing the 'tip of the iceberg' (Hawton and Rodham, 2006). Young people's motives for self-harm are discussed, as are research findings which indicate that nurses can have negative attitudes towards patients who self-harm. The article considers the implications of this for young people and identifies areas for future research.

Emergency care of children and young people

Children and young people account for a quarter of all patients treated in emergency departments in the UK, with three million children attending emergency departments every year. Emergency Care of Children and Young People prepares practitioners for the challenges of caring for children in emergency departments. Children requiring emergency care have unique and differing needs and may not respond or cooperate during an initial assessment as an adult would.