240002 CRC 1283 Block Course: An introduction to duality of Markov processes (BS) (WiSe 2020/2021)

The notion of duality of Markov processes with respect to a function has proven to be useful in a wide range of applications, reaching from interactive particle systems, queueing theory, SPDEs to population genetics. In this course we will provide a systematic treatment of such dualities. In particular, we will discuss criteria that guarantee existence and uniqueness of these relations. Furthermore, we exhibit connections between duality and stochastic monotonicity, intertwinings, and symmetries. We shall also introduce the notion of pathwise duality as it naturally appears in population genetics and interacting particle systems. Moreover, we will point out the connection of these dualities to the notion of duality with respect to a measure. Throughout, we will complement the theory with concrete examples and applications.
This course will be mostly self-contained and only basic knowledge on Markov processes will be required.