Tsallis statistics and gradually truncated Levy flight - distribution of an economical index

Tsallis postulated a generalized form for entropy and give rise to a new statistics now known as Tsallis statistics. In the present work, we compare the Tsallis statistics with the gradually truncated Levy flight, and discuss the distribution of an economical index-the Standard and Poor's 500-using the values of standard deviation as calculated by our model. We find that both statistics give almost the same distribution. Thus we feel that gradual truncation of Levy distribution, after certain critical step size for describing complex systems, is a requirement of generalized thermodynamics or similar. The gradually truncated Levy flight is based on physical considerations and bring a better physical picture of the dynamics of the whole system. Tsallis statistics gives a theoretical support. Both statistics together can be utilized for the development of a more exact portfolio theory or to understand better the complexities in human and financial behaviors. A comparison of both statistics is made. (C) 2002 Published by Elsevier B.V. B.V.

Two-dimensional nonlinear map characterized by tunable Levy flights

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Bivariate gamma-geometric law and its induced Levy process

In this article we introduce a three-parameter extension of the bivariate exponential-geometric (BEG) law (Kozubowski and Panorska, 2005) [4]. We refer to this new distribution as the bivariate gamma-geometric (BGG) law. A bivariate random vector (X, N) follows the BGG law if N has geometric distribution and X may be represented (in law) as a sum of N independent and identically distributed gamma variables, where these variables are independent of N. Statistical properties such as moment generation and characteristic functions, moments and a variance-covariance matrix are provided. The marginal and conditional laws are also studied. We show that BBG distribution is infinitely divisible, just as the BEG model is. Further, we provide alternative representations for the BGG distribution and show that it enjoys a geometric stability property. Maximum likelihood estimation and inference are discussed and a reparametrization is proposed in order to obtain orthogonality of the parameters. We present an application to a real data set where our model provides a better fit than the BEG model. Our bivariate distribution induces a bivariate Levy process with correlated gamma and negative binomial processes, which extends the bivariate Levy motion proposed by Kozubowski et al. (2008) [6]. The marginals of our Levy motion are a mixture of gamma and negative binomial processes and we named it BMixGNB motion. Basic properties such as stochastic self-similarity and the covariance matrix of the process are presented. The bivariate distribution at fixed time of our BMixGNB process is also studied and some results are derived, including a discussion about maximum likelihood estimation and inference. (C) 2012 Elsevier Inc. All rights reserved.

Levy stable distributions via associated integral transform

We present a method of generation of exact and explicit forms of one-sided, heavy-tailed Levy stable probability distributions g(alpha)(x), 0 <= x < infinity, 0 < alpha < 1. We demonstrate that the knowledge of one such a distribution g a ( x) suffices to obtain exactly g(alpha)p ( x), p = 2, 3, .... Similarly, from known g(alpha)(x) and g(beta)(x), 0 < alpha, beta < 1, we obtain g(alpha beta)( x). The method is based on the construction of the integral operator, called Levy transform, which implements the above operations. For a rational, alpha = l/k with l < k, we reproduce in this manner many of the recently obtained exact results for g(l/k)(x). This approach can be also recast as an application of the Efros theorem for generalized Laplace convolutions. It relies solely on efficient definite integration. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4709443]

The Levy Runs Dry: A Legal and Economic Analysis of EU Private Copying Levies

This article provides a legal and economic analysis of private copying levies in the EU, against the background of the Copyright Directive (2001/29), a number of recent rulings by the European Court of Justice and the recommendations presented by mediator Vitorino earlier this year. It concludes that notwithstanding these rulings and recommendations, there remains a lack of concordance on the relevance of contractual stipulations and digital rights management technologies (DRM) for setting levies, and the concept of harm. While Mr Vitorino and AG Sharpston (in the Opinion preceding VG Wort v. Kyocera) use different lines of reasoning to argue that levies raised on authorised copies would lead to double payment, the Court of Justice’s decision in VG Wort v. Kyocera seems to conclude that such copies should nonetheless be levied. If levies are to provide fair compensation for harm resulting from acts of private copying, economic analysis suggests one should distinguish between various kinds of private copies and take account of the extent to which the value said copies have for consumers can be priced into the purchase. Given the availability of DRM (including technical protection measures), the possibility of such indirect appropriation leads to the conclusion that the harm from most kinds of private copies is de minimis and gives no cause for levies. The user value of copies from unauthorised sources (e.g. from torrent networks or cyber lockers), on the other hand, cannot be appropriated indirectly by rightholders. It is, however, an open question in references for preliminary rulings pending at the Court of Justice whether these copies are included in the scope of the private copying exception or limitation and can thus be levied for. If they are not, as currently happens in several EU Member States, legal and economic analysis leads to the conclusion that the scope of private copying acts giving rise to harm susceptible of justifying levies is gradually diminishing.

Erläuterungen zu den biblischen Geschichten für die israelitische Jugend in Schule und Haus : Anhang zur Kinderbibel ; zugleich auch zu Levy-Badt's biblischer Geschichte

von Benno Badt

Michael Levy's gesammelte Aufsätze

hrsg. von A. Lewin

Nachträge und Berichtigungen zu Jacob Levy : Wörterbuch über die Talmudim und Midraschim. Sonderabdruck

von Jacob Levy und Lazarus Goldschmidt

Verzeichniss der Judaica des ... H. Levy in Hamburg

Text überwiegend in hebr. Schrift

Alphonse Levy [Rezension]

M. T.

Die Memoiren des Ascher Levy [Rezension]

Goldmann

Alphonse Levy

Rieger

Julius Rodenberg (Levy) [Illustration] : Zeichnung

Ismail Gentz