AFFILIATIONS: LYONS AND NELSON—FMA Research, Inc., Fort Collins, Colorado; ARMSTRONG—Mission Research Corporation, Nashua, New Hampshire; PASKO—The Pennsylvania State University, University Park, Pennsylvania; STANLEY—Los Alamos National Laboratory, Los Alamos, New Mexico CORRESPONDING AUTHOR: Walter A. Lyons, CCM, FMA Research, Inc., Yucca Ridge Field Station, 46050 Weld County Road 13, Fort C...

We extend the work of T. Lyons [Lyo98] and T. Lyons and Z. Qian [LQ02] to define integrals and solutions of differential equations along product of p and q rough paths, with 1/p+1/q > 1. We use this to write an Itô formula at the level of rough paths, and to see that any rough path can always be interpreted as a product of a p-geometric rough path and a p/2-geometric rough path.

Generalizing Lyons and Zheng ((13]) we study Dirichlet processes admitting a decomposition into the sum of a forward and a backward local martingale plus a bounded variation process. We develop a framework of stochastic calculus for these processes and deal with existence and uniqueness for stochastic diierential equations driven by such processes. In particular, Bessel processes turn out to be...

It is now more than 60 years since the world’s first business use of a computer, the valuation of bakery output, was rolled-out the LEO I computer at Cadby Hall in London, the headquarters of the food production and catering company J. Lyons and Company. LEO I had been designed and built as a computer to be used for business data processing by a team of engineers recruited by Lyons, with a basi...

Uniform spanning trees on finite graphs and their analogues on infinite graphs are a well-studied area. On a Cayley graph of a group, we show that they are related to the first l-Betti number of the group. Our main aim, however, is to present the basic elements of a higher-dimensional analogue on finite and infinite CW-complexes, which relate to the higher l-Betti numbers. One consequence is a ...

The history of yellow fever is discussed with relevance to the Lisbon epidemic of 1857. Robert S.D. Lyons, professor of medicine at the Catholic University Medical School in Dublin, was given leave by the rector to investigate its pathology and set off for Portugal in November. He performed autopsies and studied possible environmental factors, with negative results. The professor's "prolonged a...

The history of yellow fever is discussed with relevance to the Lisbon épidémie of 1857. Robert S.D. Lyons, prof essor ofmedicine at the Catholic University Médical School in Dublin, was given leave by the rector to investigate its pathology and set off for Portugal in November. He performed autopsies and studied possible environmental factors, with négative results. The professor's "prolonged a...

Dan Rudolph showed that for an amenable group, Γ, the generic measure-preserving action of Γ on a Lebesgue space has zero entropy. Here, this is extended to nonamenable groups. In fact, the proof shows that every action is a factor of a zero entropy action! This uses the strange phenomena that in the presence of nonamenability, entropy can increase under a factor map. The proof uses Seward’s re...