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.

Stochastic comparability and dual q-functions

In this paper we discuss the relationship and characterization of stochastic comparability, duality, and Feller–Reuter–Riley transition functions which are closely linked with each other for continuous time Markov chains. A necessary and sufficient condition for two Feller minimal transition functions to be stochastically comparable is given in terms of their density q-matrices only. Moreover, a necessary and sufficient condition under which a transition function is a dual for some stochastically monotone q-function is given in terms of, again, its density q-matrix. Finally, for a class of q-matrices, the necessary and sufficient condition for a transition function to be a Feller–Reuter–Riley transition function is also given.

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.

Safe spaces and sense of identity: views and experiences of lesbian, gay and bisexual young people

Empirical data on the life experiences of contemporary school-age lesbian, gay and bisexual (LGB) young people in Britain remains somewhat sparse. This paper reports the preliminary findings of a study conducted at a recently-initiated LGB youth Summer School. To further an appreciation of issues of concern to today's LGB teenagers, in-depth interviews were conducted with 10 Summer School participants (five female and five male, aged 15-18 years). The aim was to elicit their views and experiences relating to their need for support such as that offered by the Summer School. Themes drawn from participants' interviews are presented. Key issues included: being positioned as different by their majority heterosexual peers; feelings of isolation and loneliness in their peer groups and families; difficulties in finding others like themselves for companionship; and the importance of meeting more LGB people of their own age.