Huaizhong Zhao

Sublinear expectations arise naturally in models involving volatility uncertainty. In this talk, I will discuss the existence of invariant sublinear expectations for Markov semigroups on sublinear expectation spaces, as well as their ergodic properties. We first establish a weighted nonlinear Harris–oscillation contraction theorem, which yields large-time convergence of sublinear expectation operators in a suitably metrized complete space. We then develop probabilistic and analytic tools for studying nondegenerate (G)-diffusions with weakly dissipative drifts. As an application, we prove that the associated sublinear Markov systems are ergodic in the sense of the (0,0)-regime introduced by Feng and Zhao (2021): every invariant set of the corresponding canonical dynamical system either has capacity zero or has a complement of capacity zero. The talk is based on two joint works, one with Chunrong Feng and the other with Danyang Zhao.