Ergodicity of non-stationary stochastic processes
A talk in the Bielefeld Stochastic Afternoon series by
Huaizhong Zhao
| Abstract: | 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. This includes possible applications to a rigorous proof of stochastic resonance phenomenon in modelling of climate change proposed by physicists Benzi, Parisi, Sutera and Vulpiani. If time permits, I will mention ergodicity on sublinear expectation/capacity spaces. Within the CRC this talk is associated to the project(s): B1 |