To demonstrate more visibly the close relation between thecontinuity and integrability, a new proof for the Banach-Zareckitheorem is presented on the basis of the Radon-Nikodym theoremwhich emphasizes on measure-type properties of the Lebesgueintegral. The Banach-Zarecki theorem says that a real-valuedfunction $F$ is absolutely continuous on a finite closed intervalif and only if it is continuo...

We consider random discrete Schrόdinger operators in a strip with a potential Vω(n,a) (n a label in Z and α a finite label "across" the strip) and Vω an ergodic process. We prove that H0 -f Vω has only point spectrum with probability one under two assumptions: (1) The conditional distribution of {Kω(n,α)}n=ola l lα conditioned on {Kω}^01;allα has an absolutely continuous component with positive...

Abstract Stationary distributions of Markov processes can typically be characterized as probability measures that annihilate the generator in the sense that ∫ E Afdμ = 0 for f ∈ D(A); that is, for each such μ, there exists a stationary solution of the martingale problem for A with marginal distribution μ. This result is extended to models corresponding to martingale problems that include absolu...

We formulate and prove a general weak limit theorem for quantum random walks in one and more dimensions. With X(n) denoting position at time n, we show that X(n)/n converges weakly as n--> infinity to a certain distribution which is absolutely continuous and of bounded support. The proof is rigorous and makes use of Fourier transform methods. This approach simplifies and extends certain precedi...

Confidence interval construction for parameters of lattice distributions is considered. By using saddlepoint formulas and bootstrap calibration, we obtain relatively short intervals and bounds with O(n−3/2) coverage errors, in contrast with O(n−1) and O(n−1/2) coverage errors for normal theory intervals and bounds when the population distribution is absolutely continuous. Closed form solutions ...

We investigate the dependence on the parameters of absolutely continuous invariant measures for a family of piecewise linear piecewise expanding maps. We construct an example to show that the transitivity of the maps does not imply the convergence of those measures to the absolutely continuous invariant measure for the limit map.

We study the stability of several no-arbitrage conditions with respect to absolutely continuous, but not necessarily equivalent, changes of measure. We rst consider models based on continuous semimartingales and show that no-arbitrage conditions weaker than NA and NFLVR are always stable. Then, in the context of general semimartingale models, we show that an absolutely continuous change of meas...