A Limit Theorem for Copulas

We characterize convergence of a sequence of d-dimensional random vectors by convergence of the one-dimensional margins and of the copula. The result is applied to the approximation of portfolios modelled by t-copulas with large degrees of freedom, and to the convergence of certain dependence measures of bivariate distributions

A Continuous Time GARCH Process of Higher Order

A continuous time GARCH model of order (p,q) is introduced, which is driven by a single Lévy process. It extends many of the features of discrete time GARCH(p,q) processes to a continuous time setting. When p=q=1, the process thus defined reduces to the COGARCH(1,1) process of Klüppelberg, Lindner and Maller (2004). We give sufficient conditions for the existence of stationary solutions and show that the volatility process has the same autocorrelation structure as a continuous time ARMA process. The autocorrelation of the squared increments of the process is also investigated, and conditions ensuring a positive volatility are discussed

Continuous time volatility modelling: COGARCH versus Ornstein-Uhlenbeck models

We compare the probabilistic properties of the non-Gaussian Ornstein-Uhlenbeck based stochastic volatility model of Barndorff-Nielsen and Shephard (2001) with those of the COGARCH process. The latter is a continuous time GARCH process introduced by the authors (2004). Many features are shown to be shared by both processes, but differences are pointed out as well. Furthermore, it is shown that the COGARCH process has Pareto like tails under weak regularity conditions

A Continuous Time GARCH Process Driven by a Lévy Process: Stationarity and Second Order Behaviour

We use a discrete time analysis, giving necessary and sufficient conditions for the almost sure convergence of ARCH(1) and GARCH(1,1) discrete time models, tosuggest an extension of the (G)ARCH concept to continuous time processes. Our "COGARCH" (continuous time GARCH) model, based on a single background driving Levy process, is different from, though related to, other continuous time stochastic volatility models that have been proposed. The model generalises the essential features of discrete time GARCH processes, and is amenable to further analysis, possessing useful Markovian and stationarity properties

Some aspects of Lévy copulas

Levy processes and infinitely divisible distributions are increasingly defined in terms of their Levy measure. In order to describe the dependence structure of a multivariate Levy measure, Tankov (2003) introduced positive Levy copulas. Together with the marginal Levy measures they completely describe multivariate Levy measures on the first quadrant. In this paper, we show that any such Levy copula defines itself a Levy measure with 1-stable margins, in a canonical way. A limit theorem is obtained, characterising convergence of Levy measures with the aid of Levy copulas. Homogeneous Levy copulas are considered in detail. They correspond to Levy processes which have a time-constant Levy copula. Furthermore, we show how the Levy copula concept can be used to construct multivariat distributions in the Bondesson class with prescribed margins in the Bondesson class. The construction depends on a mapping Upsilon, recently introduced by Barndorff-Nielsen and Thorbjornsen (2004a,b) and Barndorff-Nielsen, Maejima and Sato (2004). Similar results are obtained for self-decomposable distributions and for distributions in the Thorin class

Stationarity and second order behaviour of discrete and continuous time GARCH(1,1) processes

We use a discrete time analysis, giving necessary and sufficient conditions for the almost sure convergence of ARCH(1) and GARCH(1,1) discrete time models, to suggest an extension of the (G)ARCH concept to continuous time processes. The models, based on a single background driving Levy process, are different from, though related to, other continuous time stochastic volatility models that have been proposed. Our models generalise the essential features of discrete time GARCH processes, and are amenable to further analysis, possessing useful Markovian and stationarity properties

Reactor Neutrino Experiments with a Large Liquid Scintillator Detector

We discuss several new ideas for reactor neutrino oscillation experiments with a Large Liquid Scintillator Detector. We consider two different scenarios for a measurement of the small mixing angle $\theta_{13}$ with a mobile $\bar{\nu}_e$ source: a nuclear-powered ship, such as a submarine or an icebreaker, and a land-based scenario with a mobile reactor. The former setup can achieve a sensitivity to $\sin^2 2\theta_{13} \lesssim 0.003$ at the 90% confidence level, while the latter performs only slightly better than Double Chooz. Furthermore, we study the precision that can be achieved for the solar parameters, $\sin^2 2\theta_{12}$ and $\Delta m_{21}^2$, with a mobile reactor and with a conventional power station. With the mobile reactor, a precision slightly better than from current global fit data is possible, while with a power reactor, the accuracy can be reduced to less than 1%. Such a precision is crucial for testing theoretical models, e.g. quark-lepton complementarity.Comment: 18 pages, 3 figures, 2 tables, revised version, to appear in JHEP, Fig. 1 extended, Formula added, minor changes, results unchange

Steps toward the power spectrum of matter. III. The primordial spectrum

Observed power spectrum of matter found in Papers I and II is compared with analytical power spectra. Spatially flat cold and mixed dark matter models with cosmological constant and open models are considered. The primordial power spectrum of matter is determined using the power spectrum of matter and the transfer functions of analytical models. The primordial power spectrum has a break in amplitude. We conclude that a scale-free primordial power spectrum is excluded if presently available data on the distribution of clusters and galaxies represent the true mass distribution of the Universe.Comment: LaTex (sty files added), 22 pages, 5 PostScript figures embedded, Astrophysical Journal (accepted

On the Quantitative Impact of the Schechter-Valle Theorem

We evaluate the Schechter-Valle (Black Box) theorem quantitatively by considering the most general Lorentz invariant Lagrangian consisting of point-like operators for neutrinoless double beta decay. It is well known that the Black Box operators induce Majorana neutrino masses at four-loop level. This warrants the statement that an observation of neutrinoless double beta decay guarantees the Majorana nature of neutrinos. We calculate these radiatively generated masses and find that they are many orders of magnitude smaller than the observed neutrino masses and splittings. Thus, some lepton number violating New Physics (which may at tree-level not be related to neutrino masses) may induce Black Box operators which can explain an observed rate of neutrinoless double beta decay. Although these operators guarantee finite Majorana neutrino masses, the smallness of the Black Box contributions implies that other neutrino mass terms (Dirac or Majorana) must exist. If neutrino masses have a significant Majorana contribution then this will become the dominant part of the Black Box operator. However, neutrinos might also be predominantly Dirac particles, while other lepton number violating New Physics dominates neutrinoless double beta decay. Translating an observed rate of neutrinoless double beta decay into neutrino masses would then be completely misleading. Although the principal statement of the Schechter-Valle theorem remains valid, we conclude that the Black Box diagram itself generates radiatively only mass terms which are many orders of magnitude too small to explain neutrino masses. Therefore, other operators must give the leading contributions to neutrino masses, which could be of Dirac or Majorana nature.Comment: 18 pages, 4 figures; v2: minor corrections, reference added, matches journal version; v3: typo corrected, physics result and conclusions unchange