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• W2955114501 abstract "In this chapter we study stochastic properties of spatially- and temporally-disordered structures, such as turbulence and rough surfaces, or temporal fluctuations of given time series, in scale. Experimental observables include the field increments, such as the difference in the velocity field between two points separated by a distance r, or difference of time series in a time lag r. Therefore, the lag r can be either spatial distance or a time interval. The change of the increments’ fluctuations as a function of the scale r can then be viewed as a stochastic process in a length or time scale and can, quite often, after pioneering work by Friedrich & Peinke, be mapped onto the mathematical structures of the Langevin [1] or generalised Langevin processes with jumps contributions [2]; see [3] for recent review and progresses of subject. In this chapter we discuss the stochastic analysis in scale, and provide a physical picture of the fluctuations cascade, known as cascade processes, from large to small scales. We then provide the Kramers-Moyal expansion in terms of the conditional moments of the increments. The chapter will close with the definition of “multipliers” that relate the increments’ fluctuations at scale (r_1) to those at scale (r_2), and present the Castaing equation. Finally, multiscale correlation functions will be introduced." @default.
• W2955114501 created "2019-07-12" @default.
• W2955114501 creator A5056001412 @default.
• W2955114501 date "2019-01-01" @default.
• W2955114501 modified "2023-10-16" @default.
• W2955114501 title "The Friedrich–Peinke Approach to Reconstruction of Dynamical Equation for Time Series: Complexity in View of Stochastic Processes" @default.
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• W2955114501 doi "https://doi.org/10.1007/978-3-030-18472-8_15" @default.
• W2955114501 hasPublicationYear "2019" @default.
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