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A causal multifractal stochastic equation and its statistical properties
Schmitt, F.G. (2004). A causal multifractal stochastic equation and its statistical properties. Revue des Travaux de la Station Marine de Wimereux 2003(26): 1-12
In: Dauvin, J.-C. (2003). Revue des Travaux de la Station Marine de Wimereux. Station Marine de Wimereux: Wimereux, more

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Keywords
    Fractals; Fractals; Fractals; Stochastic processes; Marine

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  • Schmitt, F.G.

Abstract
    Multiplicative cascades have been introduced in turbulence to generate random or deterministic fields having intermittent values and long-range power-law correlations. Generally this is done using discrete construction rules leading to discrete cascades. Here a causal log-normal stochastic process is introduced; its multifractal properties are demonstrated together with other properties such as the composition rule for scale dependence and stochastic differential equations for time and scale evolutions. This multifractal stochastic process is continuous in scale ratio and in time. It has a simple generating equation and can be used to generate sequentially time series of any length.

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