Change point estimation for the telegraph process observed at discrete times

The telegraph process models a random motion with finite velocity and it is usually proposed as an alternative to diffusion models. The process describes the position of a particle moving on the real line, alternatively with constant velocity $+ v$ or $-v$. The changes of direction are governed by an homogeneous Poisson process with rate $\lambda >0.$ In this paper, we consider a change point estimation problem for the rate of the underlying Poisson process by means of least squares method. The consistency and the rate of convergence for the change point estimator are obtained and its asymptotic distribution is derived. Applications to real data are also presented

Empirical L2L^2-distance test statistics for ergodic diffusions

The aim of this paper is to introduce a new type of test statistic for simple null hypothesis on one-dimensional ergodic diffusion processes sampled at discrete times. We deal with a quasi-likelihood approach for stochastic differential equations (i.e. local gaussian approximation of the transition functions) and define a test statistic by means of the empirical $L^2$-distance between quasi-likelihoods. We prove that the introduced test statistic is asymptotically distribution free; namely it weakly converges to a $\chi^2$ random variable. Furthermore, we study the power under local alternatives of the parametric test. We show by the Monte Carlo analysis that, in the small sample case, the introduced test seems to perform better than other tests proposed in literature

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

High resolution observations of the outer disk around T Cha: the view from ALMA

T Cha is a young star surrounded by a transitional disk with signatures of planet formation. We have obtained high-resolution and high-sensitivity ALMA observations of T Cha in the ${\rm CO}(3$--$2)$, ${\rm ^{13}CO}(3$--$2)$, and ${\rm CS}(7$--$6)$ emission lines to reveal the spatial distribution of the gaseous disk around the star. In order to study the dust within the disk we have also obtained continuum images at 850$\mu$m from the line-free channels. We have spatially resolved the outer disk around T Cha. Using the CO(3-2) emission we derive a radius of $\sim$230 AU. We also report the detection of the $^{13}$CO(3-2) and the CS(7-8) molecular emissions, which show smaller radii than the CO(3-2) detection. The continuum observations at 850$\mu$m allow the spatial resolution of the dusty disk, which shows two emission bumps separated by $\sim$40AU, consistent with the presence of a dust gap in the inner regions of the disk, and an outer radius of $\sim$80AU. Therefore, T Cha is surrounded by a compact dusty disk and a larger and more diffuse gaseous disk, as previously observed in other young stars. The continuum intensity profiles are different at both sides of the disk suggesting possible dust asymmetries. We derive an inclination of i(deg)=67$\pm$5, and a position angle of PA (deg)= 113$\pm$6, for both the gas and dust disks. The comparison of the ALMA data with radiative transfer models shows that the gas and dust components can only be simultaneously reproduced when we include a tapered edge prescription for the surface density profile. The best model suggests that most of the disk mass is placed within a radius of $R<$ 50AU. Finally, we derive a dynamical mass for the central object of $M_{*}$=1.5$\pm$0.2M$_{\odot}$, comparable to the one estimated with evolutionary models for an age of $\sim$10Myr.Comment: 5 pages, 5 figures, accepted for publication in A&A Letter

Thaumetopoea Pinivora Treitschke, 1834, Thaumetopoidae nou per a la fauna de Catalunya (Lepidoptera)

Se da cuenta del hallazgo en Cataluña (Els Coms de Das, Baixa Cerdanya, Pirineo oriental) de Thaumetopoea pinivora Treitschke, 1834, Thaumetopoeidae nuevo para la región. Se exponent los aspectos más interesantes de su bionomía y se pone al día la distribución de esta especie en la Península Ibérica.Thaumetopoea pinivora Treitschke, 1834, Thaumetopoidae new for Catalonia (Lepidoptera). In this paper the authors report the found in Catalonia (Els Coms de Das, Baixa Cerdanya, Pirineu oriental) of Thaumetopoea pinivora Treitschke, 1834, Thaumetopoeidae new for the area. We expose the more interesting aspects of its bionomy and actualize its distribution in the lberian fauna

Cantharellus lilacinopruinatus Hermitte, Eyssart. & Poumarat, a Catalunya i les Illes Balears

Es descriu , comenta i il·lustra un interessant t áxon de les CantharelI ácies: Cantharellus Iilacinopruinatus Hermitte, Eyssart. & Poumarat, recol·lectat per primer cop a Catalunya i Illes Balears.An interesting taxon of Cantharellaceae: Cantharellus lilacinop ruinatu s Hennitte, Eyssart. & Poumarat, previou sly unrecorded in Catalonia and the Balearic Island s, is described, commented and illustrated.Se describe, comenta e ilustra un interesante taxón de las Cantareláceas: Cantharellus lilacinopruinatus Hennitte, Eyssart. & Poumarat, recolectado por primera vez en Cataluña y Baleares

Harmonic damped oscillators with feedback. A Langevin study

We consider a system in direct contact with a thermal reservoir and which, if left unperturbed, is well described by a memory-less equilibrium Langevin equation of the second order in the time coordinate. In such conditions, the strength of the noise fluctuations is set by the damping factor, in accordance with the Fluctuation and Dissipation theorem. We study the system when it is subject to a feedback mechanism, by modifying the Langevin equation accordingly. Memory terms now arise in the time evolution, which we study in a non-equilibrium steady state. Two types of feedback schemes are considered, one focusing on time shifts and one on phase shifts, and for both cases we evaluate the power spectrum of the system's fluctuations. Our analysis finds application in feedback cooled oscillators, such as the Gravitational Wave detector AURIGA.Comment: 17 page