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)

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

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

Spectroscopy of D-type asteroids

We have performed a spectroscopic survey of 19 D-type asteroids. Comparison with previous photometry shows excellent agreement. Although the majority have similar colors to cometary nuclei, no cometary emission bands were present in any of the spectra. Absorption bands sporadically appearing were apparently due to stellar objects, and no features inherent to the asteroids were observed

Boundary-crossing identities for diffusions having the time-inversion property

We review and study a one-parameter family of functional transformations, denoted by (S (β)) β∈ℝ, which, in the case β<0, provides a path realization of bridges associated to the family of diffusion processes enjoying the time-inversion property. This family includes Brownian motions, Bessel processes with a positive dimension and their conservative h-transforms. By means of these transformations, we derive an explicit and simple expression which relates the law of the boundary-crossing times for these diffusions over a given function f to those over the image of f by the mapping S (β), for some fixed β∈ℝ. We give some new examples of boundary-crossing problems for the Brownian motion and the family of Bessel processes. We also provide, in the Brownian case, an interpretation of the results obtained by the standard method of images and establish connections between the exact asymptotics for large time of the densities corresponding to various curves of each family

Sputtering of Oxygen Ice by Low Energy Ions

Naturally occurring ices lie on both interstellar dust grains and on celestial objects, such as those in the outer solar system. These ices are continu- ously subjected to irradiation by ions from the solar wind and/or cosmic rays, which modify their surfaces. As a result, new molecular species may form which can be sputtered off into space or planetary atmospheres. We determined the experimental values of sputtering yields for irradiation of oxygen ice at 10 K by singly (He+, C+, N+, O+ and Ar+) and doubly (C2+, N2+ and O2+) charged ions with 4 keV kinetic energy. In these laboratory experiments, oxygen ice was deposited and irradiated by ions in an ultra high vacuum chamber at low temperature to simulate the environment of space. The number of molecules removed by sputtering was observed by measurement of the ice thickness using laser interferometry. Preliminary mass spectra were taken of sputtered species and of molecules formed in the ice by temperature programmed desorption (TPD). We find that the experimental sputtering yields increase approximately linearly with the projectile ion mass (or momentum squared) for all ions studied. No difference was found between the sputtering yield for singly and doubly charged ions of the same atom within the experimental uncertainty, as expected for a process dominated by momentum transfer. The experimental sputter yields are in good agreement with values calculated using a theoretical model except in the case of oxygen ions. Preliminary studies have shown molecular oxygen as the dominant species sputtered and TPD measurements indicate ozone formation.Comment: to be published in Surface Science (2015

Ground-based monitoring of comet 67P/Churyumov-Gerasimenko gas activity throughout the <i>Rosetta</i> mission

Simultaneously to the ESA Rosetta mission, a world-wide ground-based campaign provided measurements of the large scale activity of comet 67P/Churyumov-Gerasimenko through measurement of optically active gas species and imaging of the overall dust coma. We present more than two years of observations performed with the FORS2 low resolution spectrograph at the VLT, TRAPPIST, and ACAM at the WHT. We focus on the evolution of the CN production, as a tracer of the comet activity. We find that it is asymmetric with respect to perihelion and different from that of the dust. The CN emission is detected for the first time at 1.34 au pre-perihelion and production rates then increase steeply to peak about two weeks after perihelion at (1.00±0.10) ×1025 molecules s−1, while the post-perihelion decrease is more shallow. The evolution of the comet activity is strongly influenced by seasonal effects, with enhanced CN production when the Southern hemisphere is illuminated