Auto-tail dependence coefficients for stationary solutions of linear stochastic recurrence equations and for GARCH(1,1)

We examine the auto-dependence structure of strictly stationary solutions of linear stochastic recurrence equations and of strictly stationary GARCH(1, 1) processes from the point of view of ordinary and generalized tail dependence coefficients. Since such processes can easily be of infinite variance, a substitute for the usual auto-correlation function is needed

Limiting behaviour of Fréchet means in the space of phylogenetic trees

As demonstrated in our previous work on T4, the space of phylogenetic trees with four leaves, the topological structure of the space plays an important role in the non-classical limiting behaviour of the sample Fréchet means in T4. Nevertheless, the techniques used in that paper cannot be adapted to analyse Fréchet means in the space Tm of phylogenetic trees with m(⩾5)m(⩾5) leaves. To investigate the latter, this paper first studies the log map of Tm. Then, in terms of a modified version of this map, we characterise Fréchet means in Tm that lie in top-dimensional or co-dimension one strata. We derive the limiting distributions for the corresponding sample Fréchet means, generalising our previous results. In particular, the results show that, although they are related to the Gaussian distribution, the forms taken by the limiting distributions depend on the co-dimensions of the strata in which the Fréchet means lie

Efficient estimation in the semiparametric normal regression-copula model with a focus on QTL mapping

The semiparametric normal copula model is studied with a correlation matrix that depends on a covariate. The bivariate version of this regression-copula model has been proposed for statistical analysis of Quantitative Trait Loci (QTL) via twin data. Appropriate linear combinations of Van der Waerden’s normal scores rank correlation coefficients yield $\sqrt{n}$-consistent estimators of the coefficients in the correlation function, i.e. of the regression parameters. They are used to construct semiparametrically efficient estimators of the regression parameters

Convergence to stable laws for multidimensional stochastic recursions: the case of regular matrices

Given a sequence $(M_{n},Q_{n})_{n\ge 1}$ of i.i.d.\ random variables with generic copy $(M,Q) \in GL(d, \R) \times \R^d$, we consider the random difference equation (RDE) $$R_{n}=M_{n}R_{n-1}+Q_{n},$$ $n\ge 1$, and assume the existence of $\kappa >0$ such that \lim_{n \to \infty}(\E{\norm{M_1 ... M_n}^\kappa})^{\frac{1}{n}} = 1 . We prove, under suitable assumptions, that the sequence $S_n = R_1 + ... + R_n$, appropriately normalized, converges in law to a multidimensional stable distribution with index $\kappa$. As a by-product, we show that the unique stationary solution $R$ of the RDE is regularly varying with index $\kappa$, and give a precise description of its tail measure. This extends the prior work http://arxiv.org/abs/1009.1728v3 .Comment: 15 page

Two-proton small-angle correlations in central heavy-ion collisions: a beam-energy and system-size dependent study

Small-angle correlations of pairs of protons emitted in central collisions of Ca + Ca, Ru + Ru and Au + Au at beam energies from 400 to 1500 MeV per nucleon are investigated with the FOPI detector system at SIS/GSI Darmstadt. Dependences on system size and beam energy are presented which extend the experimental data basis of pp correlations in the SIS energy range substantially. The size of the proton-emitting source is estimated by comparing the experimental data with the output of a final-state interaction model which utilizes either static Gaussian sources or the one-body phase-space distribution of protons provided by the BUU transport approach. The trends in the experimental data, i.e. system-size and beam energy dependences, are well reproduced by this hybrid model. However, the pp correlation function is found rather insensitive to the stiffness of the equation of state entering the transport model calculations.Comment: 9 pages, 8 figures, accepted at Eur. Phys. Journ.

Direct comparison of phase-space distributions of K- and K+ mesons in heavy-ion collisions at SIS energies - evidence for in-medium modifications of kaons ?

The ratio of K- to K+ meson yields has been measured in the systems RuRu at 1.69 A GeV, Ru+Zr at 1.69 A GeV, and Ni+Ni at 1.93 A GeV incident beam kinetic energy. The yield ratio is observed to vary across the measured phase space. Relativistic transport-model calculations indicate that the data are best understood if in-medium modifications of the kaons are taken into account.Comment: 14 pages including 3 figure

Isospin dependence of relative yields of K+K^+ and K0K^0 mesons at 1.528 AGeV

Results on $K^+$ and $K^0$ meson production in $^{96}_{44}$Ru + $^{96}_{44}$Ru and $^{96}_{40}$Zr + $^{96}_{40}$Zr collisions at a beam kinetic energy of 1.528$A$ GeV, measured with the FOPI detector at GSI-Darmstadt, are investigated as a possible probe of isospin effects in high density nuclear matter. The measured double ratio ($K^+/K^0$)$_{Ru}$/($K^+/K^0$)$_{Zr}$ is compared to the predictions of a thermal model and a Relativistic Mean Field transport model using two different collision scenarios and under different assumptions on the stiffness of the symmetry energy. We find a good agreement with the thermal model prediction and the assumption of a soft symmetry energy for infinite nuclear matter while more realistic transport simulations of the collisions show a similar agreement with the data but also exhibit a reduced sensitivity to the symmetry term.Comment: 5 pages, 3 figures. accepted for publication in Phys. Rev.

Charged pion production in 4496^{96}_{44}Ru+4496^{96}_{44}Ru collisions at 400A and 1528A MeV

We present transverse momentum and rapidity spectra of charged pions in central Ru + Ru collisions at 400$A$ and 1528$A$ MeV. The data exhibit enhanced production at low transverse momenta compared to the expectations from the thermal model that includes the decay of $\Delta(1232)$-resonances and thermal pions. Modification of the $\Delta$-spectral function and the Coulomb interaction are necessary to describe the detailed shape of the transverse momentum spectra. Within the framework of the thermal model, the freeze-out radii of pions are similar at both beam energies. The IQMD model reproduces the shapes of the transverse momentum and rapidity spectra of pions, but the predicted absolute yields are larger than in the measurements, especially at lower beam energy.Comment: 12 pages, 11 figure

Excitation function of elliptic flow in Au+Au collisions and the nuclear matter equation of state

We present measurements of the excitation function of elliptic flow at midrapidity in Au+Au collisions at beam energies from 0.09 to 1.49 GeV per nucleon. For the integral flow, we discuss the interplay between collective expansion and spectator shadowing for three centrality classes. A complete excitation function of transverse momentum dependence of elliptic flow is presented for the first time in this energy range, revealing a rapid change with incident energy below 0.4 AGeV, followed by an almost perfect scaling at the higher energies. The equation of state of compressed nuclear matter is addressed through comparisons to microscopic transport model calculations.Comment: 10 pages, 4 eps figures, submitted for publication. Data files will be available at http://www.gsi.de/~fopiwww/pub

Flow angle from intermediate mass fragment measurements

Directed sideward flow of light charged particles and intermediate mass fragments was measured in different symmetric reactions at bombarding energies from 90 to 800 AMeV. The flow parameter is found to increase with the charge of the detected fragment up to Z = 3-4 and then turns into saturation for heavier fragments. Guided by simple simulations of an anisotropic expanding thermal source, we show that the value at saturation can provide a good estimate of the flow angle, $\Theta_{flow}$, in the participant region. It is found that $\Theta_{flow}$ depends strongly on the impact parameter. The excitation function of $\Theta_{flow}$ reveals striking deviations from the ideal hydrodynamical scaling. The data exhibit a steep rise of \Theta_{\flow} to a maximum at around 250-400 AMeV, followed by a moderate decrease as the bombarding energy increases further.Comment: 28 pages Revtex, 6 figures (ps files), to appear in Nucl.Phys.