Let a class F of densities be given. We draw an i.i.d. sample from a density f which may or may not be in F . After every n, one must make a guess whether f ∈ F or not. A class is almost surely discernible if there exists such a sequence of classification rules such that for any f , we make finitely many errors almost surely. In this paper several results are given that allow one to decide whet...

Chung and Erdös (1951) are among the first to prove some form of an almost sure local limit theorem (cf. Csáki et al., 1993). Here we propose a formulation of such statements and discuss related problems. Surely, Frits will enjoy them. c ©2001, June 19.

In order to extend the modeling capabilities of rewriting systems, it is rather natural to consider that the ring of rules can be subject to some probabilistic laws. Considering rewrite rules subject to probabilities leads to numerous questions about the underlying notions and results. We focus here on the problem of termination of a set of probabilistic rewrite rules. A probabilistic rewrite s...