Speaker
Description
This talk is concerned with quasi-stationary distributions (QSDs) of continuous-time Markov chains (CTMCs) with extinction in a setting that embraces reaction networks. QSDs describe the long-term behavior of such stochastic systems conditioned not to go extinct.
QSDs have a long history in probability theory, and this talk draws from this rich history. The focus is on CTMCs on the non-negative integers with a local jump structure. This local jump structure enforces (among other things) a recursive characterization of QSDs, the existence of an extremal QSD, and the existence of a sequence of Karlin-McGregor-type polynomials of increasing degree that characterizes Kingman’s parameter. The local jump structure is naturally implied by the structure of reaction networks. Some of these results and their importance will be explained in a (presumably) non-technical way.
Furthermore, the results will be illustrated by examples from reaction network theory, and the intuition of the audience will be tested, and why our intuition might fail, will be discussed.
