Orateur
Description
In this talk we will put the main focus on applications of the concept of duality to quite concrete stochastic models. In particular, we will shift focus from the abstract duality framework on the level of generators to consider stochastic processes in a pathwise set up. We will discuss how dual processes may often be interpreted in a strong pathwise sense as forward- and backward pictures of the same underlying stochastic models. This is particularly evident in many classical models of population genetics, such as the Wright-Fisher model, where one process describes the forward evolution of an allele frequency, and the dual process its genealogy. Thanks to this connection, duality may be applied to easily calculate quantities of interest such as fixation probabilities, as we will demonstrate.
We will discuss several such applications in classical population genetics and in population models with dormancy, as well as in interacting particle systems, and discuss connections between strong pathwise dualities and generator dualities.