ON STABILITY OF DIFFUSIONS WITH COMPOUND-POISSON JUMPS

We give fairly easy conditions under which a multidimensional diffusion with jumps of compound-Poisson type possess several global-stability properties: (exponential) ergodicity, (exponential) β-mixing property, and also boundedness of moments. These are important to statistical inference under long-time asymptotics. The underlying technique used in this article is based on Masuda (2007), but we here utilize an explicit “T-chain”, which enables us to include almost arbitrary finite-jump parts under nondegeneracy of the diffusion part without reference to topological continuity of the original transition semigroup.