The purpose of this paper is to extend recent mean as well as a.e. convergence results of Derriennic (1983), Liggett (1985) and Schürger (1986) to multiparameter processes X which satisfy a strong almost subadditivity condition and have certain monotonicity properties. If X is even strongly...

Suppose that (X(n)) is a finite adapted sequence of d-dimensional random variables defined on some filtered probability space ([Omega], F, (Fn), P). We obtain conditions which are necessary and sufficient for the existence of a probability measure Q equivalent to P (which we call an equivalent...

Let Z be a stochastic process of the form Z(t)=Z(0)exp([mu]t+X(t)-<X>t/2) where Z(0)0, [mu] are constants, and X is a continuous local martingale having a deterministic quadratic variation <X> such that <X>t--[infinity] as t--[infinity]. We show that the mantissa (base b) of Z(t) (denoted by M(b)(Z(t))...</x></x></x>

Based on multiparameter subadditive ergodic theorems of Akcoglu and Krengel (1981) and Schürger (1988) we derive an almost sure limit theorem for families of random matrices with a multiparameter which satisfy a supermultiplicativity condition. This gives a multiparameter analogue of results of...

A random variable X is digit-regular (respectively, significant-digit-regular) if the probability that every block of k given consecutive digits (significant digits) appears in the b-adic expansion of X approaches b-k as the block moves to the right, for all integers b1 and k[greater-or-equal,...