Markov Processes with Identical Bridges

Let X and Y be time-homogeneous Markov processes with common state space E, and assume that the transition kernels of X and Y admit densities with respect to suitable reference measures. We show that if there is a time t>0 such that, for each x\in E, the conditional distribution of (X_s)_{0 < s < t}, given X_0 = x = X_t, coincides with the conditional distribution of (Y_s)_{0 < s < t}, given Y_0 = x = Y_t, then the infinitesimal generators of X and Y are related by [L^Y]f = \psi^{-1}[L^X](\psi f)-\lambda f, where \psi is an eigenfunction of L^X with eigenvalue \lambda. Under an additional continuity hypothesis, the same conclusion obtains assuming merely that X and Y share a ``bridge'' law for one triple (x,t,y). Our work entends and clarifies a recent result of I. Benjamini and S. Lee.Comment: 12 pages. See also http://math.ucsd.edu/~pfitz/preprints.htm

On a result of D.W. Stroock

We show how to modify an argument of D. W. Stroock to show that an additive map from one separable Banach space to another, that is "universally Gaussian measurable", must be continuous (hence linear)

On measuring the impact of hyperlinks on reading

We increasingly spend a vast amount of time on the Web and much of that time is spent reading. One of the main differences between reading non-Web based text and reading on the Web is the presence of hyperlinks within the text, linking various related Web content and Web pages together. Some researchers and commentators have claimed that hyperlinks hinder reading because they are a distraction that may have a negative effect on the reader’s ability to process the text. However, very few controlled experiments have been conducted to verify these claims.In the experiments documented here we utilise eye tracking as a new methodology for examining how we read hyperlinked text. An eye tracker was used to observe participant’s behaviour while reading. The results showed that hyperlinked text did not generally have a negative impact upon reading behaviour. However, participants did show a tendency to re-read sentences that contained hyperlinked uncommon (low frequency) words. This suggests that hyperlinks highlight important information to the reader and the hyperlinks add additional content which for more difficult concepts, invites rereading of the preceding text

Errata for Stochastic calculus for symmetric Markov processes

This erratum corrects the article arXiv:0806.2044 published in Ann. Probab. 36 (2008) 931--970Comment: Published in at http://dx.doi.org/10.1214/11-AOP684 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Absolute continuity of symmetric Markov processes

We study Girsanov's theorem in the context of symmetric Markov processes, extending earlier work of Fukushima-Takeda and Fitzsimmons on Girsanov transformations of ``gradient type.'' We investigate the most general Girsanov transformation leading to another symmetric Markov process. This investigation requires an extension of the forward-backward martingale method of Lyons-Zheng, to cover the case of processes with jumps.Comment: Published by the Institute of Mathematical Statistics (http://www.imstat.org) in the Annals of Probability (http://www.imstat.org/aop/) at http://dx.doi.org/10.1214/00911790400000043

Magnetically asymmetric interfaces in a (LaMnO3_3)/(SrMnO3_3) superlattice due to structural asymmetries

Polarized neutron reflectivity measurements of a ferromagnetic [(LaMnO$_3$)$_{11.8}$/(SrMnO$_3$)$_{4.4}$]$_6$ superlattice reveal a modulated magnetic structure with an enhanced magnetization at the interfaces where LaMnO$_3$ was deposited on SrMnO$_3$ (LMO/SMO). However, the opposite interfaces (SMO/LMO) are found to have a reduced ferromagnetic moment. The magnetic asymmetry arises from the difference in lateral structural roughness of the two interfaces observed via electron microscopy, with strong ferromagnetism present at the interfaces that are atomically smooth over tens of nanometers. This result demonstrates that atomic-scale roughness can destabilize interfacial phases in complex oxide heterostructures.Comment: 5 pages, 4 figure