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.

Chattels: I have bought it all for you

Outlines the ways by which personal property can be acquired through the gift of chattels, referring to case law including the Court of Appeal rulings in Re Cole (A Bankrupt) and Re Kirkland, and through the declaration of trust, with reference to the Chancery Division ruling in Rowe v Prance. Compares this to the use of constructive trusts or proprietary estoppel to secure assets and considers the need to prove detrimental reliance.