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,...

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 &supk; as the block moves to the right, for all integers b 1 and k ? 1. Necessary...

The paper generalizes and refines the Fundamental Theorem of Asset Pricing of Dalang, Morton and Willinger in the following two respects: (a) the result is extended to a model with portfolio constraints; (b) versions of the no-arbitrage criterion based on the bang-bang principle in control...

It is shown that moments of negative order as well as positive non- integral order of a nonnegative random variable X can be expressed by the Laplace transform of X. Applying these results of certain first passage times gives explicit formulae for moments of suprema of Bessel processes as well...

Let S=(S_t), t=0,1,...,T (T being finite), be an adapted R^d-valued process. Each component process of S might be interpreted as the price process of a certain security. A trading strategy H=(H_t), t= 1,...,T, is a predictable R^d-valued process. A strategy H is called extreme if it represents a...

In this paper we consider families (Xm,n) of random variables which satisfy a subadditivity condition of the form X0,n+m <= X0,n + Xn,n+m + Yn,n+m, m, n >= 1. The main purpo is to give conditions which are sufficient for the a.e. convergence of ((1/n)X0,n). Restricting ourselves to the case when (X0,n) has certain monotonicity...</=>

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>