Least squares volatility change point estimation for partially observed diffusion processes

A one dimensional diffusion process $X=\{X_t, 0\leq t \leq T\}$, with drift $b(x)$ and diffusion coefficient $\sigma(\theta, x)=\sqrt{\theta} \sigma(x)$ known up to $\theta>0$, is supposed to switch volatility regime at some point $t^*\in (0,T)$. On the basis of discrete time observations from $X$, the problem is the one of estimating the instant of change in the volatility structure $t^*$ as well as the two values of $\theta$, say $\theta_1$ and $\theta_2$, before and after the change point. It is assumed that the sampling occurs at regularly spaced times intervals of length $\Delta_n$ with $n\Delta_n=T$. To work out our statistical problem we use a least squares approach. Consistency, rates of convergence and distributional results of the estimators are presented under an high frequency scheme. We also study the case of a diffusion process with unknown drift and unknown volatility but constant

On random flights with non-uniformly distributed directions

This paper deals with a new class of random flights $\underline{\bf X}_d(t),t>0,$ defined in the real space $\mathbb{R}^d, d\geq 2,$ characterized by non-uniform probability distributions on the multidimensional sphere. These random motions differ from similar models appeared in literature which take directions according to the uniform law. The family of angular probability distributions introduced in this paper depends on a parameter $\nu\geq 0$ which gives the level of drift of the motion. Furthermore, we assume that the number of changes of direction performed by the random flight is fixed. The time lengths between two consecutive changes of orientation have joint probability distribution given by a Dirichlet density function. The analysis of $\underline{\bf X}_d(t),t>0,$ is not an easy task, because it involves the calculation of integrals which are not always solvable. Therefore, we analyze the random flight $\underline{\bf X}_m^d(t),t>0,$ obtained as projection onto the lower spaces $\mathbb{R}^m,m<d,$ of the original random motion in $\mathbb{R}^d$. Then we get the probability distribution of $\underline{\bf X}_m^d(t),t>0.$ Although, in its general framework, the analysis of $\underline{\bf X}_d(t),t>0,$ is very complicated, for some values of $\nu$, we can provide some results on the process. Indeed, for $\nu=1$, we obtain the characteristic function of the random flight moving in $\mathbb{R}^d$. Furthermore, by inverting the characteristic function, we are able to give the analytic form (up to some constants) of the probability distribution of $\underline{\bf X}_d(t),t>0.$Comment: 28 pages, 3 figure

An assessment of vortex detection criteria for 2C-2D PIV data

The aim of the article is to propose a robust and reliable engineering method for identifying and characterizing vortical structures within a flow field measured with a classic twocomponent PIV measurement system. Some of the most popular vortex-detection criteria are briefly presented for comparison purposes. Many of these fail if spurious vectors are present within the flow field due to poor PIV image quality. The proposed method was tested both on synthetic images of ideal vortices, having different spatial resolutions and different noise levels in order to perform a parametric assessment, and on real PIV images of a four-bladed rotor wake

Silicon isotopic abundance toward evolved stars and its application for presolar grains

Galactic chemical evolution (GCE) is important for understanding the composition of the present-day interstellar medium (ISM) and of our solar system. In this paper, we aim to track the GCE by using the 29Si/30Si ratios in evolved stars and tentatively relate this to presolar grain composition. We used the APEX telescope to detect thermal SiO isotopologue emission toward four oxygen-rich M-type stars. Together with the data retrieved from the Herschel science archive and from the literature, we were able to obtain the 29Si/30Si ratios for a total of 15 evolved stars inferred from their optically thin 29SiO and 30SiO emission. These stars cover a range of masses and ages, and because they do not significantly alter 29Si/30Si during their lifetimes, they provide excellent probes of the ISM metallicity (or 29Si/30Si ratio) as a function of time. The 29Si/30Si ratios inferred from the thermal SiO emission tend to be lower toward low-mass oxygen-rich stars (e.g., down to about unity for W Hya), and close to an interstellar or solar value of 1.5 for the higher-mass carbon star IRC+10216 and two red supergiants. There is a tentative correlation between the 29Si/30Si ratios and the mass-loss rates of evolved stars, where we take the mass-loss rate as a proxy for the initial stellar mass or current stellar age. This is consistent with the different abundance ratios found in presolar grains. We found that older objects (up to possibly 10 Gyr old) in our sample trace a previous, lower 29Si/30Si value of about 1. Material with this isotopic ratio is present in two subclasses of presolar grains, providing independent evidence of the lower ratio. Therefore, the 29Si/30Si ratio derived from the SiO emission of evolved stars is a useful diagnostic tool for the study of the GCE and presolar grains.Comment: 7 pages, 4 figure

A proto brown dwarf candidate in Taurus

Aims. We search for brown dwarfs at the Class 0/I evolutionary stage, or proto brown dwarfs. Methods. We present a multi wavelength study, ranging from optical at 0.8 μm to radio wavelengths at 6 cm, of a cool, very faint, and red multiple object, SSTB213 J041757, detected by Spitzer toward the Barnard 213 dark cloud, in Taurus. Results. The SED of SSTB213 J041757 displays a clear excess at long wavelengths resembling that of a Class I object. The mid-IR source has two possible counterparts, A and B, in the near-IR and optical images, and the 350 μm observations detect clear extended emission, presumably from an envelope around the two sources. The position of A & B in the (Ic− J) versus (J − [3.6]) colour-colour diagram is consistent with them being Galactic sources and not extragalactic contaminants. A proper-motion study confirms this result for A, while it is inconclusive for B. The temperature and mass of the two possible central objects, according to COND evolutionary models, range between 1550−1750 K and 3−4 M_(Jupiter), and 950−1300 K and 1−2 M_(Jupiter), for A and B, respectively. The integrated SED provides bolometric temperatures and luminosities of 280 K and 0.0034 L_⊙, assuming that the emission at wavelengths > 5 μm is associated with component A, and 150 K and 0.0033 L_⊙, assuming that the emission at wavelengths > 5 μm is associated with component B, which would imply the SSTB213 J041757 object has a luminosity well below the luminosity of other very low luminosity objects discovered up to date. Conclusions. With these characteristics, SSTB213 J041757 seems to be a promising, and perhaps double, proto brown dwarf candidate

First detection of thermal radio jets in a sample of proto-brown dwarf candidates

We observed with the JVLA at 3.6 and 1.3 cm a sample of 11 proto-brown dwarf candidates in Taurus in a search for thermal radio jets driven by the most embedded brown dwarfs. We detected for the first time four thermal radio jets in proto-brown dwarf candidates. We compiled data from UKIDSS, 2MASS, Spitzer, WISE and Herschel to build the Spectral Energy Distribution (SED) of the objects in our sample, which are similar to typical Class~I SEDs of Young Stellar Objects (YSOs). The four proto-brown dwarf candidates driving thermal radio jets also roughly follow the well-known trend of centimeter luminosity against bolometric luminosity determined for YSOs, assuming they belong to Taurus, although they present some excess of radio emission compared to the known relation for YSOs. Nonetheless, we are able to reproduce the flux densities of the radio jets modeling the centimeter emission of the thermal radio jets using the same type of models applied to YSOs, but with corresponding smaller stellar wind velocities and mass-loss rates, and exploring different possible geometries of the wind or outflow from the star. Moreover, we also find that the modeled mass outflow rates for the bolometric luminosities of our objects agree reasonably well with the trends found between the mass outflow rates and bolometric luminosities of YSOs, which indicates that, despite the "excess" centimeter emission, the intrinsic properties of proto-brown dwarfs are consistent with a continuation of those of very low mass stars to a lower mass range. Overall, our study favors the formation of brown dwarfs as a scaled-down version of low-mass stars.Comment: 18 pages, 8 figures, 14 tables, accepted by the Astrophysical Journa

Unexpectedly large mass loss during the thermal pulse cycle of the red giant R Sculptoris!

The asymptotic giant branch star R Sculptoris is surrounded by a detached shell of dust and gas. The shell originates from a thermal pulse during which the star undergoes a brief period of increased mass loss. It has hitherto been impossible to constrain observationally the timescales and mass-loss properties during and after a thermal pulse - parameters that determine the lifetime on the asymptotic giant branch and the amount of elements returned by the star. Here we report observations of CO emission from the circumstellar envelope and shell around R Sculptoris with an angular resolution of 1.3 arcsec. What was hitherto thought to be only a thin, spherical shell with a clumpy structure, is revealed to contain a spiral structure. Spiral structures associated with circumstellar envelopes have been seen previously, from which it was concluded that the systems must be binaries. Using the data, combined with hydrodynamic simulations, we conclude that R Sculptoris is a binary system that underwent a thermal pulse approximately 1800 years ago, lasting approximately 200 years. About 0.003 Msun of mass was ejected at a velocity of 14.3 km s-1 and at a rate approximately 30 times higher than the prepulse mass-loss rate. This shows that approximately 3 times more mass is returned to the interstellar medium during and immediately after a pulse than previously thought.Comment: Accepted by Natur