A new perspective on quasi-stationary distributions (Paul Dupuis -- Brown University)

The quasi-stationary distribution (QSD) of a Markov process $X(t)$ with respect to a set $D$ characterizes the distribution of $X(T)$, given that $X(t)$ remains in $D$ for $t \in [0,T]$ and $T$ is large. Although they have a long history in probability, QSDs are not nearly as well understood as their (linear) cousins, stationary distributions. The first part of the talk will review some of the subtleties in characterizing, analyzing and approximating QSDs. The second part will present a recently derived representation for QSDs in terms of ergodic optimal control problems and describe how the control representation can be used to resolve some of these difficulties.