Incremental similarity and turbulence
Teoriâ veroâtnostej i ee primeneniâ, Tome 61 (2016) no. 3, pp. 588-595

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This paper discusses the mathematical representation of an empirically observed phenomenon, referred to as incremental similarity. We discuss this feature from the viewpoint of stochastic processes and present a variety of nontrivial examples, including those that are relevant to turbulence modeling.
Keywords: universality, normal inverse Gaussian, ${BSS}/{LSS}$ type, trawl processes
Mots-clés : alpha-stable processes.
O. E. Barndorff-Nielsen; E. Hedevang; J. Schmiegel. Incremental similarity and turbulence. Teoriâ veroâtnostej i ee primeneniâ, Tome 61 (2016) no. 3, pp. 588-595. http://geodesic.mathdoc.fr/item/TVP_2016_61_3_a9/
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[1] Barndorff-Nielsen O. E., “Models for non-Gaussian variation in turbulence”, Proc. Roy. Soc. London A, 368 (1979), 501–520 | DOI | MR | Zbl

[2] Barndorff-Nielsen O. E., “Stationary infinitely divisible processes”, Brazilian J. Probab. Statist., 25 (2011), 294–322 | DOI | MR | Zbl

[3] Barndorff-Nielsen O. E., Benth F. E., Veraart A., “Recent advances in ambit stochastics with a view towards tempo-spatial stochastic volatility/intermittency”, Banach Centre Publications, 104 (2015), 25–60 | DOI | MR | Zbl

[4] Barndorff-Nielsen O. E., Blæsild P., Schmiegel J., “A parsimonious and universal description of turbulent velocity increments”, Eur. Phys. J. B, 41 (2004), 345–363 | DOI | MR

[5] Barndorff-Nielsen O. E., Schmiegel J., Change of time and universal laws in turbulence, Technical report, Thiele Centre, University of Aarhus, Denmark, 2007–2008

[6] Barndorff-Nielsen O. E., Schmiegel J., “Brownian semistationary processes and volatility/intermittency”, Advanced Financial Modelling, eds. Albrecher H., Rungaldier W., Schachermeyer W., de Gruyter, Berlin, 2009, 1–26 | MR

[7] Birnir B., “The Kolmogorov–Obukhov statistical theory of turbulence”, J. Nonlinear Sci., 0938-8974 (2013), 1–32 | MR

[8] Birnir B., The Kolmogorov–Obukhov Theory of Turbulence, Springer, Heidelberg, 2013 | MR | Zbl

[9] Birnir B., “The Kolmogorov–Obukhov–She-Leveque scaling in Turbulence”, Com. Pure Appl. Anal., 13 (2014), 1737–1757 | DOI | MR | Zbl

[10] Hedevang E., Schmiegel J., “A causal continuous-time stochastic model for the turbulent energy cascade in a helium jet flow”, J. Turbulence, 14:11 (2014), 1–26 | DOI | MR

[11] Márquez J. U., Schmiegel J., Modelling turbulent time series by BSS-processes. The Fascination of Probability, Statistics, and Their Applications, eds. Podolskij M., Stelzer R., Thorbjørnsen S., Veraart A. E., Springer, Heidelberg, 2015

[12] Podolskij M., “Ambit Fields: survey and new challenges”, XI Symposium on Probability and Stochastic Processes, eds. Mena R. H., Pardo J. C., Rivero V., Bravo G. U., 2014, 241–279