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.

General Harris regularity criterion for non-linear Markov branching processes

We extend the Harris regularity condition for ordinary Markov branching process to a more general case of non-linear Markov branching process. A regularity criterion which is very easy to check is obtained. In particular, we prove that a super-linear Markov branching process is regular if and only if the per capita offspring mean is less than or equal to I while a sub-linear Markov branching process is regular if the per capita offspring mean is finite. The Harris regularity condition then becomes a special case of our criterion.

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.

I wanna be a protocol: online media and electronic structures of kinship

Heidegger famously identified Modernity with a technological leveling of being to a single order of a “standing reserve.” In a radically different tone, Gilles Deleuze articulated a single “plane of immanence” within which ontological distinctions between mind and body, God and world, interiority and exteriority become indiscernible. Taking such philosophical declarations as points of departure, this panel will consider how a collapse of ontological distinction emerged as a thematic and structural trope in literary and cinematic modernisms. We hope to consider how writers and film-makers of the 20th c. utilize the resources of their media to ask “the question of being” that troubled their philosophical contemporaries and heirs. In this vein, we will examine how these modernist ontologies of immanence describe the crisis of a subject saturated and eclipsed by a world which comprises her while also remaining strange or opaque. Papers will ask what is lost with the departure of a distinctly human sense of “being” and how the historical arrival of an alternative ontological order may be evident in the lived experience of modernity. In this sense, the relationship to departures and arrivals becomes the modern subject’s suspicion that he is unable to do either vis á vis the world.