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A multitype Dawson-Watanabe process is conditioned, in subcritical and critical cases, on non-extinction in the remote future. On every nite time interval, its distribution law is absolutely continuous with respect to the law of the unconditioned process. A martingale problem characterization is also given. The explicit form of the Laplace functional of the conditioned process is used to obtain several results on the long time behaviour of the mass of the conditioned and unconditioned processes. The general case is considered first, where the mutation matrix which modelizes the interaction between the types, is irreducible. Several two-type models with decomposable mutation matrices are also analysed.
Der vorliegende Beitrag knüpft an die in Potsdam seit 2001 durchgeführte Langzeitstudie an und untersucht die aktuelle Situation auf dem formellen Beteiligungsmarkt in Deutschland nach dem Ausbruch der Finanzkrise. Neben den allgemeinen Gegebenheiten des Marktes werden vor allem die Finanzierungsbedingungen sowie das Investitionsverhalten einzelner Beteiligungsgesellschaften analysiert. In den Jahren 2008 - 2009 zeigt sich einerseits eine weitestgehend unveränderte Struktur der Refinanzierungsquellen. Privatpersonen und Banken sowie der öffentliche Sektor nehmen weiterhin einen hohen Stellenwert ein. Andererseits werden deutliche Veränderungen der strukturellen Merkmale, wie auch im Investitionsverhalten einzelner Beteiligungsgesellschaften deutlich. Besonders auffällig für die Branche sind das Rationalisierungsbestreben beim Einsatz von Investmentmanagern sowie die zunehmende Spätphasenspezialisierung. Aus dem festgestellten Konsolidierungs- und Reifeprozess erwächst die Herausforderung und offene Frage, wie der Markt eine solche strukturelle Angebotslücke im Frühphasensegment begegnen will. Auch das Einwerben neuer Finanzmittel sowie die aktuellen Exit-Bedingungen werden in der vorliegenden Studie kritisch beleuchtet. Als ein reizvolles Instrument zur Reduzierung der aufgezeigten Problemfelder wird dabei die aktuell unterentwickelte Syndizierung von Beteiligungsinvestitionen angesehen. Die effizientere Ausgestaltung derartiger Finanzierungsstrukturen sollte dazu beitragen, dass das private Beteiligungskapital künftig stärker bei der Transformation betrieblicher Forschung und Entwicklung zum Einsatz gelangt.
The accelerated life time model is considered. First, test procedures for testing the parameter of a parametric acceleration function is investigated; this is done under the assumption of parametric and nonparametric baseline distribution. Further, based on nonparametric estimators for regression functions tests are proposed for checking whether a parametric acceleration function is appropriate to model the influence of the covariates. Resampling procedures are discussed for the realization of these methods. Simulations complete the considerations.
We consider the problem of testing whether the density of a mul- tivariate random variable can be expressed by a prespecified copula function and the marginal densities. The proposed test procedure is based on the asymptotic normality of the properly standardized integrated squared distance between a multivariate kernel density estimator and an estimator of its expectation under the hypothesis. The test of independence is a special case of this approach.
We consider an infinite system of hard balls in Rd undergoing Brownian motions and submitted to a pair potential with infinite range and quasi polynomial decay. It is modelized by an infinite-dimensional Stochastic Differential Equation with an infinite-dimensional local time term. Existence and uniqueness of a strong solution is proven for such an equation with deterministic initial condition. We also show that the set of all equilibrium measures, solution of a Detailed Balance Equation, coincides with the set of canonical Gibbs measures associated to the hard core potential.
We consider a system of infinitely many hard balls in Rd undergoing Brownian motions and submitted to a smooth pair potential. It is modelized by an infinite-dimensional Stochastic Differential Equation with a local time term. We prove that the set of all equilibrium measures, solution of a Detailed Balance Equation, coincides with the set of canonical Gibbs measures associated to the hard core potential added to the smooth interaction potential.
The aim of this paper is to demonstrate that nonparametric smoothing methods for estimating functions can be an useful tool in the analysis of life time data. After stating some basic notations we will present a data example. Applying standard parametric methods to these data we will see that this approach fails - basic features of the underlying functions are not reflected by their estimates. Our proposal is to use nonparametric estimation methods. These methods are explained in section 2. Nonparametric approaches are better in the sense that they are more flexible, and misspecifications of the model are avoided. But, parametric models have the advantage that the parameters can be interpreted. So, finally, we will formulate a test procedure to check whether a parametric or a nonparametric model is appropriate.
We give a necessary and sufficient condition for the existence of an increasing coupling of N (N >= 2) synchronous dynamics on S-Zd (PCA). Increasing means the coupling preserves stochastic ordering. We first present our main construction theorem in the case where S is totally ordered; applications to attractive PCAs are given. When S is only partially ordered, we show on two examples that a coupling of more than two synchronous dynamics may not exist. We also prove an extension of our main result for a particular class of partially ordered spaces.
We first introduce some coupling of a finite number of Probabilistic Cellular Automata dynamics (PCA), preserving the stochastic ordering. Using this tool, for a general attractive probabilistic cellular automata on SZd, where S is finite, we prove that a condition (A) is equivalent to the (time-) convergence towards equilibrium of this Markovian parallel dynamics, in the uniform norm, exponentially fast. This condition (A) means the exponential decay of the influence from the boundary for the invariant measures of the system restricted to finite ‘box’-volume. For a class of reversible PCA dynamics on {−1, +1}Zd , with a naturally associated Gibbsian potential ϕ, we prove that a Weak Mixing condition for ϕ implies the validity of the assumption (A); thus the ‘exponential ergodicity’ of the dynamics towards the unique Gibbs measure associated to ϕ holds. On some particular examples of this PCA class, we verify that our assumption (A) is weaker than the Dobrushin-Vasershtein ergodicity condition. For some special PCA, the ‘exponential ergodicity’ holds as soon as there is no phase transition.