An introduction to duality of Markov processes
A talk in the CRC Block Course series by
Fernando Cordero, Sebastian Hummel
| Abstract: | 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, queue-
ing 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.
Dates: 02.11.2020 from 10:15 to 11:45 03.11.2020 from 10:15 to 11:45 04.11.2020 from 10:15 to 11:45 05.11.2020 from 10:15 to 11:45 Join the Zoom Meeting: Meeting ID: 965 6417 6078 Passcode: 915888 |