Probability Seminar: Vladislav Vysotskiy - Stationary random walks with a switch
| Dates: | 12 March 2025 |
|---|
| Times: | 15:00 - 16:00 |
|---|
| What is it: | Seminar |
|---|
| Organiser: | Department of Mathematics |
|---|
|
|
Vladislav Vysotskiy (University of Sussex) will speak at the Probability seminar.
Title: Stationary random walks with a switch
Abstract: A switching random walk, commonly known under the misnomer `oscillating random walk', is a real-valued Markov chain whose distribution of increments depends only on the sign of the current position. We will present an explicit invariant measure of such chain, and prove its uniqueness (up to a constant factor) under the minimal assumption that the switching walk crosses the zero level infinitely often. Moreover, we give sufficient conditions for the topological recurrence and prove the topological irreducibility of the switching walk on an appropriate state space. Among other things, our proof establishes a relationship between the classical stationary distributions of renewal processes and stationarity of these processes with respect to the Lebesgue measure.
Travel and Contact Information
Find event
Frank Adams 2
Alan Turing Building
Manchester
