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.

Existence, recurrence and equilibrium properties of Markov branching processes with instantaneous immigration

Attention has recently focussed on stochastic population processes that can undergo total annihilation followed by immigration into state j at rate αj. The investigation of such models, called Markov branching processes with instantaneous immigration (MBPII), involves the study of existence and recurrence properties. However, results developed to date are generally opaque, and so the primary motivation of this paper is to construct conditions that are far easier to apply in practice. These turn out to be identical to the conditions for positive recurrence, which are very easy to check. We obtain, as a consequence, the surprising result that any MBPII that exists is ergodic, and so must possess an equilibrium distribution. These results are then extended to more general MBPII, and we show how to construct the associated equilibrium distributions.

Translating Nietzsche, mediating literature: Alexander Tille and the limits of Anglo-German intercultural transfer

Dr. Alexander Tille (1866–1912) was one of the key-figures in Anglo-German intercultural transfer towards the end of the 19th century. As a lecturer in German at Glasgow University he was the first to translate and edit Nietzsche’s work into English. Writers such as W. B. Yeats were influenced by Nietzsche and used Tille’s translations. Tille’s social Darwinist reading of the philosopher’s oeuvre, however, had a narrowing impact on the reception of Nietzsche in the Anglo-Saxon world for decades. Through numerous publications Tille disseminated knowledge about British authors (e.g., Robert Louis Stevenson, William Wordsworth) in Germany and about German authors (e.g., Johann Wolfgang von Goethe) in Britain. His role as mediator also extended into areas such as history, religion, and industry. During the Boer war, however, Tille’s outspoken pro-German nationalism brought him in conflict with his British host society. After being physically attacked by his students he returned to Germany and published a highly anglophobic monograph. Tille personifies the paradox of Anglo-German relations in the pre-war years, which deteriorated despite an increase in intercultural transfer and knowledge about the respective Other. [From the Author]