Ergodicity of non-stationary stochastic processes

2023.4.7 10:00 N613

I will discuss the ergodicity of two kinds of non-stationary processes:random periodic processes and random quasi-periodic processes.I will describe periodic measures, quasi-periodic measures and the way to lift them on cylinders, then to construct invariant measures. I will discuss their ergodicity, while they are certainly not mixing. I will also present results on the existence of periodic measures and quasi-periodic measures and more generally entrance measures for a wide class of stochastic differential equations, which could be degenerate and possibly expanding. If time permits, I will mention ergodicity on sublinear expectation spaces.