Non-parametric Bayesian drift estimation for stochastic differential equations

We consider non-parametric Bayesian estimation of the drift coefficient of a one-dimensional stochastic differential equation from discrete-time observations on the solution of this equation. Under suitable regularity conditions that are weaker than those previosly suggested in the literature, we establish posterior consistency in this context. Furthermore, we show that posterior consistency extends to the multidimensional setting as well, which, to the best of our knowledge, is a new result in this setting.Comment: 27 page

The ATHENA X-ray Integral Field Unit (X-IFU)

The X-ray Integral Field Unit (X-IFU) is the high resolution X-ray spectrometer of the ESA Athena X-ray observatory. Over a field of view of 5' equivalent diameter, it will deliver X-ray spectra from 0.2 to 12 keV with a spectral resolution of 2.5 eV up to 7 keV on ∼ 5" pixels. The X-IFU is based on a large format array of super-conducting molybdenum-gold Transition Edge Sensors cooled at ∼ 90 mK, each coupled with an absorber made of gold and bismuth with a pitch of 249 μm. A cryogenic anti-coincidence detector located underneath the prime TES array enables the non X-ray background to be reduced. A bath temperature of ∼ 50 mK is obtained by a series of mechanical coolers combining 15K Pulse Tubes, 4K and 2K Joule-Thomson coolers which pre-cool a sub Kelvin cooler made of a 3He sorption cooler coupled with an Adiabatic Demagnetization Refrigerator. Frequency domain multiplexing enables to read out 40 pixels in one single channel. A photon interacting with an absorber leads to a current pulse, amplified by the readout electronics and whose shape is reconstructed on board to recover its energy with high accuracy. The defocusing capability offered by the Athena movable mirror assembly enables the X-IFU to observe the brightest X-ray sources of the sky (up to Crab-like intensities) by spreading the telescope point spread function over hundreds of pixels. Thus the X-IFU delivers low pile-up, high throughput (< 50%), and typically 10 eV spectral resolution at 1 Crab intensities, i.e. A factor of 10 or more better than Silicon based X-ray detectors. In this paper, the current X-IFU baseline is presented, together with an assessment of its anticipated performance in terms of spectral resolution, background, and count rate capability. The X-IFU baseline configuration will be subject to a preliminary requirement review that is scheduled at the end of 2018

Adaptive estimation of the stationary density of a stochastic differential equation driven by a fractional Brownian motion

International audienceWe build and study a data-driven procedure for the estimation of the stationary density f of an additive fractional SDE. To this end, we also prove some new concentrations bounds for discrete observations of such dynamics in stationary regime