Velocity probability density functions of high Reynolds number turbulence

Castaing, B.; Gagne, Yves; Hopfinger, Emil J.

doi:10.1016/0167-2789(90)90035-n

Cited by 716 publications

(790 citation statements)

References 26 publications

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“…While in [12] D 1 and D 2 were also found to be linear and quadratic functions of x, respectively, the values given for the coefficients γ, α and β were different from the ones given here in equation (25).…”

Section: Discussioncontrasting

confidence: 79%

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Evidence of Markov properties of high frequency exchange rate data

Renner

Peinke

Friedrich

2001

Physica A: Statistical Mechanics and its Applications

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We present a stochastic analysis of a data set consisiting of 10 6 quotes of the US Doller -German Mark exchange rate. Evidence is given that the price changes x(τ ) upon different delay times τ can be described as a Markov process evolving in τ . Thus, the τ -dependence of the probability density function (pdf) p(x, τ ) on the delay time τ can be described by a Fokker-Planck equation, a gerneralized diffusion equation for p(x, τ ). This equation is completely determined by two coefficients D 1 (x, τ ) and D 2 (x, τ ) (drift-and diffusion coefficient, respectively). We demonstrate how these coefficients can be estimated directly from the data without using any assumptions or models for the underlying stochastic process. Furthermore, it is shown that the solutions of the resulting Fokker-Planck equation describe the empirical pdfs correctly, including the pronounced tails.

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Section: Discussioncontrasting

confidence: 79%

“…According to (25), the drift coefficient D 1 is completely antisymmetric in x (D 1 (−x) = −D 1 (x)), while the diffusion coefficient D 2 is symmetric in x. The resulting Fokker-Planck equation (10) for the pdf p(x, τ ) is symmetric in x.…”

Section: Discussionmentioning

confidence: 99%

Evidence of Markov properties of high frequency exchange rate data

Renner

Peinke

Friedrich

2001

Physica A: Statistical Mechanics and its Applications

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“…[25], in which are presented probability density functions with an aspect very similar to some of the distributions presented herein. This underlines the surmised application of the our theoretical model to turbulence models.…”

Section: Acknowledgmentsmentioning

confidence: 72%

On superstatistical multiplicative-noise processes

Queirós¹

2008

Braz. J. Phys.

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In this article we analyse the long-term probability density function of non-stationary dynamical processes with time varying multiplicative noise exponents which are enclosed inwards the Feller class of processes. The update in the value of the exponent occurs in the same conditions as presented by BECK and COHEN for superstatistics. Moreover, we are able to provide a dynamical scenario for the emergence of a generalisation of the Weibull distribution previously introduced.

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“…where W η is a stochastic variable [15,44]. We assume that the cascading process starts from a large scale, L, where by starting the iterating process would eventually tend to small scales (ℓ < L).…”

Section: Model and Analysismentioning

confidence: 99%

“…Once, the infinitely divisible cascades [15][16][17] in hydrodynamic turbulence was confirmed to be statistically scale-invariant, one important motivation for multifractal formulation to become prominent was established [18,19]. Multifractal models have been implemented in various fields of sciences ranging from biology, geology, social to finance, e.g.…”

Section: Introductionmentioning

confidence: 99%

Coupled uncertainty provided by a multifractal random walker

et al. 2015

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The aim here is to study the concept of pairing multifractality between time series possessing nonGaussian distributions. The increasing number of rare events creates "criticality". We show how the pairing between two series is affected by rare events, which we call "coupled criticality". A method is proposed for studying the coupled criticality born out of the interaction between two series, using the bivariate multifractal random walk (BiMRW). This method allows studying dependence of the coupled criticality on the criticality of each individual system. This approach is applied to data sets of gold & oil markets, and inflation & unemployment.

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Velocity probability density functions of high Reynolds number turbulence

Cited by 716 publications

References 26 publications

Evidence of Markov properties of high frequency exchange rate data

Evidence of Markov properties of high frequency exchange rate data

On superstatistical multiplicative-noise processes

Coupled uncertainty provided by a multifractal random walker

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