|A causal multifractal stochastic equation and its statistical properties|In: The European Physical Journal B. EDP Sciences: Les Ulis, more
|Also published as |
- 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, more
Fractals; Fractals; Fractals; Stochastic processes; Marine
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.