On the sub-exponential mixing rate for a class of Markov diffusions
The authors prove sub-exponential bounds on the \(\beta\)-mixing rate of convergence to the invariant measure for one-dimensional diffusions with a unit diffusion coefficient. They state that a generalization to the finite-dimensional, nonunit diffusion case is possible. The results of the paper improve upon those of \textit{M. N. Malyshkin} [Theory Probab. Appl. 45, No.~3, 466--479 (2000); translation from Teor. Veroyatn. Primen. 45, No. 3, 489--504 (2000; Zbl 0994.60062)]. To obtain the bounds, the authors use the method of ``quasi-Lyapunov functions''.
scientific article; zbMATH DE number 2183334