arXiv subjects

Jürgen Schmiegel

Publications and source records attributed to Jürgen Schmiegel.

4 recordsLinked to original sources

arXiv2015

Assessing Relative Volatility/Intermittency/Energy Dissipation

We introduce the notion of relative volatility/intermittency and demonstrate how relative volatility statistics can be used to estimate consistently the temporal variation of volatility/intermittency when the data of interest are generated by a non-semimartingale, or a Brownian semistationary process in particular. This estimation method is motivated by the assessment of relative energy dissipation in empirical data of turbulence, but it is also applicable in other areas. We develop a probabilistic asymptotic theory for realised relative power variations of Brownian semistationary processes, and introduce inference methods based on the theory. We also discuss how to extend the asymptotic theory to other classes of processes exhibiting stochastic volatility/intermittency. As an empirical application, we study relative energy dissipation in data of atmospheric turbulence.

math.ST↗

arXiv2013

A causal continuous-time stochastic model for the turbulent energy cascade in a helium jet flow

We discuss continuous cascade models and their potential for modelling the energy dissipation in a turbulent flow. Continuous cascade processes, expressed in terms of stochastic integrals with respect to Lévy bases, are examples of ambit processes. These models are known to reproduce experimentally observed properties of turbulence: The scaling and self-scaling of the correlators of the energy dissipation and of the moments of the coarse-grained energy dissipation. We compare three models: a normal model, a normal inverse Gaussian model and a stable model. We show that the normal inverse Gaussian model is superior to both, the normal and the stable model, in terms of reproducing the distribution of the energy dissipation; and that the normal inverse Gaussian model is superior to the normal model and competitive with the stable model in terms of reproducing the self-scaling exponents. Furthermore, we show that the presented analysis is parsimonious in the sense that the self-scaling exponents are predicted from the one-point distribution of the energy dissipation, and that the shape of these distributions is independent of the Reynolds number.

cond-mat.stat-mech↗

arXiv2008

Lévy-based growth models

In the present paper, we give a condensed review, for the nonspecialist reader, of a new modelling framework for spatio-temporal processes, based on Lévy theory. We show the potential of the approach in stochastic geometry and spatial statistics by studying Lévy-based growth modelling of planar objects. The growth models considered are spatio-temporal stochastic processes on the circle. As a by product, flexible new models for space--time covariance functions on the circle are provided. An application of the Lévy-based growth models to tumour growth is discussed.

math.ST↗

arXiv1999

Artificiality of multifractal phase transitions

A multifractal phase transition is associated to a nonanalyticity in the generalised dimensions. We show that its occurrence is an artifact of the asymptotic scaling behaviour of integral moments and that it is not observed in an analysis based on differential n-point correlation densities.

chao-dyn↗