Dispersive Billiards and Brownian Motion Are Statistically Indistinguishable

摘要

The uniform Doeblin condition in the d bar-convergence theorem in a paper by Eloranta (1990) is relaxed into milder and more explicit conditions. In doing this the authors also present a general d bar-convergence theorem for processes with jump distributions being arbitrary mixtures of absolutely continuous and discrete type and treat the cases of compact and noncompact statespace in a unified way. The applicability of the theorem is thus further enchanced which they illustrate by extending a result by Bunimovich and Sinai on billiards. In particular, the strengthening of their invariance principle paves the road to general stability results in the sense of the alpha-congruence.