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 |