Linear maps on the space of all bounded observables preserving maximal deviation

In this paper we determine all the bijective linear maps on the space of bounded observables which preserve a fixed moment or the variance. Nonlinear versions of the corresponding results are also presented.Comment: 27 pages. To appear in J. Funct. Ana

Karhunen-Lo\`eve expansion for a generalization of Wiener bridge

We derive a Karhunen-Lo\`eve expansion of the Gauss process $B_t - g(t)\int_0^1 g'(u)\,d B_u$, $t\in[0,1]$, where $(B_t)_{t\in[0,1]}$ is a standard Wiener process and $g:[0,1]\to R$ is a twice continuously differentiable function with $g(0) = 0$ and $\int_0^1 (g'(u))^2\,d u =1$. This process is an important limit process in the theory of goodness-of-fit tests. We formulate two special cases with the function $g(t)=\frac{\sqrt{2}}{\pi}\sin(\pi t)$, $t\in[0,1]$, and $g(t)=t$, $t\in[0,1]$, respectively. The latter one corresponds to the Wiener bridge over $[0,1]$ from $0$ to $0$.Comment: 25 pages, 1 figure. The appendix is extende

Wavelet-Based Detection of Outliers in Poisson INAR(1) Time Series

The presence of outliers or discrepant observations has a negative impact in time series modelling. This paper considers the problem of detecting outliers, additive or innovational, single, multiple or in patches, in count time series modelled by first-order Poisson integer-valued autoregressive, PoINAR(1), models. To address this problem, two wavelet-based approaches that allow the identification of the time points of outlier occurrence are proposed. The effectiveness of the proposed methods is illustrated with synthetic as well as with an observed dataset

Uniqueness of the embedding continuous convolution semigroup of a Gaussian probability measure on the affine group and an application in mathematical finance

Let {mu((i))(t)}(t >= 0) (i = 1, 2) be continuous convolution semigroups (c.c.s.) of probability measures on Aff(1) (the affine group on the real line). Suppose that mu((1))(1) = mu((2))(1). Assume furthermore that {mu((1))(t)}(t >= 0) is a Gaussian c.c.s. (in the sense that its generating distribution is a sum of a primitive distribution and a second-order differential operator). Then mu((1))(1) = mu((2))(1) for all t >= 0. We end up with a possible application in mathematical finance

55 Cancri e's occultation captured with CHEOPS

Past occultation and phase-curve observations of the ultra-short period super-Earth 55 Cnc e obtained at visible and infrared wavelengths have been challenging to reconcile with a planetary reflection and emission model. In this study, we analyse a set of 41 occultations obtained over a two-year timespan with the CHEOPS satellite. We report the detection of 55 Cnc e's occultation with an average depth of $12\pm3$ ppm. We derive a corresponding 2-$\sigma$ upper limit on the geometric albedo of $A_g < 0.55$ once decontaminated from the thermal emission measured by Spitzer at 4.5$\mu$m. CHEOPS's photometric performance enables, for the first time, the detection of individual occultations of this super-Earth in the visible and identifies short-timescale photometric corrugations likely induced by stellar granulation. We also find a clear 47.3-day sinusoidal pattern in the time-dependent occultation depths that we are unable to relate to stellar noise, nor instrumental systematics, but whose planetary origin could be tested with upcoming JWST occultation observations of this iconic super-Earth.Comment: In press. Accepted for publication in Astronomy and Astrophysics on 13 October 2022. 10 pages, 7 figures and 3 table

Detection of the tidal deformation of WASP-103b at 3 σ with CHEOPS

This article has an erratum: https://doi.org/10.1051/0004-6361/202142196eContext. Ultra-short period planets undergo strong tidal interactions with their host star which lead to planet deformation and orbital tidal decay. Aims. WASP-103b is the exoplanet with the highest expected deformation signature in its transit light curve and one of the shortest expected spiral-in times. Measuring the tidal deformation of the planet would allow us to estimate the second degree fluid Love number and gain insight into the planet’s internal structure. Moreover, measuring the tidal decay timescale would allow us to estimate the stellar tidal quality factor, which is key to constraining stellar physics. Methods. We obtained 12 transit light curves of WASP-103b with the CHaracterising ExOplanet Satellite (CHEOPS) to estimate the tidal deformation and tidal decay of this extreme system. We modelled the high-precision CHEOPS transit light curves together with systematic instrumental noise using multi-dimensional Gaussian process regression informed by a set of instrumental parameters. To model the tidal deformation, we used a parametrisation model which allowed us to determine the second degree fluid Love number of the planet. We combined our light curves with previously observed transits of WASP-103b with the Hubble Space Telescope (HST) and Spitzer to increase the signal-to-noise of the light curve and better distinguish the minute signal expected from the planetary deformation. Results. We estimate the radial Love number of WASP-103b to be hf = 1.59−0.53+0.45. This is the first time that the tidal deformation is directly detected (at 3 σ) from the transit light curve of an exoplanet. Combining the transit times derived from CHEOPS, HST, and Spitzer light curves with the other transit times available in the literature, we find no significant orbital period variation for WASP-103b. However, the data show a hint of an orbital period increase instead of a decrease, as is expected for tidal decay. This could be either due to a visual companion star if this star is bound, the Applegate effect, or a statistical artefact. Conclusions. The estimated Love number of WASP-103b is similar to Jupiter’s. This will allow us to constrain the internal structure and composition of WASP-103b, which could provide clues on the inflation of hot Jupiters. Future observations with James Webb Space Telescope can better constrain the radial Love number of WASP-103b due to their high signal-to-noise and the smaller signature of limb darkening in the infrared. A longer time baseline is needed to constrain the tidal decay in this system

Hint of an exocomet transit in the CHEOPS light curve of HD 172555

HD 172555 is a young (~20 Myr) A7V star surrounded by a 10 au wide debris disk suspected to be replenished partly by collisions between large planetesimals. Small evaporating transiting bodies, that is exocomets, have also been detected in this system by spectroscopy. After β Pictoris, this is another example of a system possibly witnessing a phase of the heavy bombardment of planetesimals. In such a system, small bodies trace dynamical evolution processes. We aim to constrain their dust content by using transit photometry. We performed a 2-day-long photometric monitoring of HD 172555 with the CHEOPS space telescope in order to detect shallow transits of exocomets with a typical expected duration of a few hours. The large oscillations in the light curve indicate that HD 172555 is a δ Scuti pulsating star. After removing those dominating oscillations, we found a hint of a transient absorption. If fitted with an exocomet transit model, it would correspond to an evaporating body passing near the star at a distance of 6.8±1.4R★ (or 0.05±0.01 au) with a radius of 2.5 km. These properties are comparable to those of the exocomets already found in this system using spectroscopy, as well as those found in the β Pic system. The nuclei of the Solar System's Jupiter family comets, with radii of 2-6 km, are also comparable in size. This is the first piece of evidence of an exocomet photometric transit detection in the young system of HD 172555