116 research outputs found
Generalized explicit inversive generators of small p-weight degree
Using rational functions to generate pseudorandom number sequences is a popular research topic. In this paper, we study bounds on additive character sums of a new explicit generator based on rational functions with small p-weight degree. This extends the class of functions where a nontrivial character sum bound is known
On lattice profile of the elliptic curve linear congruential generators
Lattice tests are quality measures for assessing the intrinsic structure of pseudorandom number generators. Recently a new lattice test has been introduced by Niederreiter and Winterhof. In this paper, we present a general inequality that is satisfied by any periodic sequence. Then, we analyze the behavior of the linear congruential generators on elliptic curves (EC-LCG) under this new lattice test and prove that the EC-LCG passes it up to very high dimensions. We also use a result of Brandstätter and Winterhof on the linear complexity profile related to the correlation measure of order k to present lower bounds on the linear complexity profile of some binary sequences derived from the EC-LCG
Consistency of Markov chain quasi-Monte Carlo on continuous state spaces
The random numbers driving Markov chain Monte Carlo (MCMC) simulation are
usually modeled as independent U(0,1) random variables. Tribble [Markov chain
Monte Carlo algorithms using completely uniformly distributed driving sequences
(2007) Stanford Univ.] reports substantial improvements when those random
numbers are replaced by carefully balanced inputs from completely uniformly
distributed sequences. The previous theoretical justification for using
anything other than i.i.d. U(0,1) points shows consistency for estimated means,
but only applies for discrete stationary distributions. We extend those results
to some MCMC algorithms for continuous stationary distributions. The main
motivation is the search for quasi-Monte Carlo versions of MCMC. As a side
benefit, the results also establish consistency for the usual method of using
pseudo-random numbers in place of random ones.Comment: Published in at http://dx.doi.org/10.1214/10-AOS831 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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