By Mark Podolskij, Robert Stelzer, Steen Thorbjørnsen, Almut E. D. Veraart

ISBN-10: 3319258249

ISBN-13: 9783319258249

Collecting jointly twenty-three self-contained articles, this quantity offers the present learn of a few popular scientists in either likelihood idea and facts in addition to their quite a few purposes in economics, finance, the physics of wind-blown sand, queueing structures, chance evaluate, turbulence and different areas.

The contributions are devoted to and encouraged through the learn of Ole E. Barndorff-Nielsen who, because the early Nineteen Sixties, has been and remains to be a truly energetic and influential researcher engaged on quite a lot of vital problems.

The themes lined contain, yet usually are not restricted to, econometrics, exponential households, Lévy methods and infinitely divisible distributions, restrict concept, mathematical finance, random matrices, probability overview, statistical inference for stochastic approaches, stochastic research and optimum regulate, time sequence, and turbulence. The publication could be of curiosity to researchers and graduate scholars in probability, facts and their applications.

**Read Online or Download The Fascination of Probability, Statistics and their Applications: In Honour of Ole E. Barndorff-Nielsen PDF**

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**Additional info for The Fascination of Probability, Statistics and their Applications: In Honour of Ole E. Barndorff-Nielsen**

**Example text**

The model reproduces the empirical sdf for the whole range of observed frequencies. The excellent agreement for the sdf translates directly to the corresponding second order structure functions that are shown in Fig. 2a. Note that the sdf (or equivalently the second order structure function) is the basic observable that determines the parameters of the (2, x0 )-gamma kernel g used for the simulation. The excellent agreement for the sdf (and S2 ) strongly indicates that the parametric choice of a (2, x0 )-gamma kernel is appropriate.

We have shown that the PDF (11) of the velocity differences in turbulence consists of a continuous distribution convolved with a discrete one. 1 of 26 B. Birnir turbulence. 1. Remarkably, all of this follows from the Navier-Stokes equations when generic noise is added to it (4). Acknowledgments This work was supported by a grant from the UC Santa Barbara Academic Senate and a Chair of Excellence at Universidad de Carlos III, Madrid, whose support is gratefully acknowledged. References 1. : The Physics of Blown Sand and Desert Dunes.

This strongly fluctuating behaviour, which is far away from what might be expected in a Gaussian framework, is called the intermittency of the energy dissipation. The traditional characterisation of the intermittent behaviour of the energy dissipation refers to the coarse grained field amplitude over a time horizon T ε(T, t) = 1 T t+T /2 t−T /2 εs ds. (4) It has been shown in numerous publications that the moments of the coarse grained energy dissipation follow a scaling law in the inertial range for large Reynolds numbers (5) E ε(T, t)n ∝ T −ξ(n) where the positive multifractal scaling exponents ξ(n) are expected to be universal in the limit of very large Reynolds number (cf.

### The Fascination of Probability, Statistics and their Applications: In Honour of Ole E. Barndorff-Nielsen by Mark Podolskij, Robert Stelzer, Steen Thorbjørnsen, Almut E. D. Veraart

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