Generalized solutions and distributional shadows for Dirac equations

We discuss the application of recent results on generalized solutions to the Cauchy problem for hyperbolic systems to Dirac equations with external fields. In further analysis we focus on the question of existence of associated distributional limits and derive their explicit form in case of free Dirac fields with regularizations of initial values corresponding to point-like probability densities

Augmented GARCH sequences: Dependence structure and asymptotics

The augmented GARCH model is a unification of numerous extensions of the popular and widely used ARCH process. It was introduced by Duan and besides ordinary (linear) GARCH processes, it contains exponential GARCH, power GARCH, threshold GARCH, asymmetric GARCH, etc. In this paper, we study the probabilistic structure of augmented $\mathrm {GARCH}(1,1)$ sequences and the asymptotic distribution of various functionals of the process occurring in problems of statistical inference. Instead of using the Markov structure of the model and implied mixing properties, we utilize independence properties of perturbed GARCH sequences to directly reduce their asymptotic behavior to the case of independent random variables. This method applies for a very large class of functionals and eliminates the fairly restrictive moment and smoothness conditions assumed in the earlier theory. In particular, we derive functional CLTs for powers of the augmented GARCH variables, derive the error rate in the CLT and obtain asymptotic results for their empirical processes under nearly optimal conditions.Comment: Published in at http://dx.doi.org/10.3150/07-BEJ120 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Cultural variation of views on effective Crew Resource Management skills

While it is generally agreed in the aviation community, that effective crew resource management (CRM) skills are an indispensable condition for a safe and efficient flight operation, there seems to be a wider range of views on what behaviors constitute effective crew performance. Within a European project an evaluation tool for CRM skills called NOTECHS was developed with four categories: Co-operation, Leadership and Managerial Skills, Situation Awareness and Decision Making. In a study to examine its suitability as a standard for CRM skills in different European regions the cultural robustness of the method was tested. 105 instructor pilots from 15 different airlines representing 12 European countries participated. The participants evaluated crew behaviors in eight video scenarios with the NOTECHS method. According to variance analytical results, regional differences in Europe seem to affect the ratings of CRM-skills only to a small degree. Cultural differences are confounded with other background variables, such as English language proficiency, work experience, instructor experience and attitudes. These background variables seem to have stronger effects on views of effective CRM behaviors than culture per se. Results of the analyses are discussed with respect to cultural robustness of the NOTECHS method