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...

In this article we give a classi cation of the binary, simple, ω−categorical structures with SU−rank 1 and trivial pregeometry. This is done both by showing that they satisfy certain extension properties, but also by noting that they may be approximated by the almost sure theory of some sets of nite structures equipped with a probability measure. This study give results about general almost sur...

In two-player finite-state stochastic games of partial observation on graphs, in every state of the graph, the players simultaneously choose an action, and their joint actions determine a probability distribution over the successor states. The game is played for infinitelymany rounds and thus the players construct an infinite path in the graph. We consider reachability objectives where the firs...

The paper studies the exponential and non–exponential convergence rate to zero of solutions of scalar linear convolution Itô-Volterra equations in which the noise intensity depends linearly on the current state. By exploiting the positivity of the solution, various upper and lower bounds in first mean and almost sure sense are obtained, including Liapunov exponents .