A multifractal random walk

Details A multifractal random walk A multifractal random walk

2000-05-24

arxiv.org/abs/cond-mat/0005405v1

Physics

Condensed Matter

5 pages, 4 figures, uses RevTex

Scientific paper

10.1103/PhysRevE.64.026103

We introduce a class of multifractal processes, referred to as Multifractal Random Walks (MRWs). To our knowledge, it is the first multifractal processes with continuous dilation invariance properties and stationary increments. MRWs are very attractive alternative processes to classical cascade-like multifractal models since they do not involve any particular scale ratio. The MRWs are indexed by few parameters that are shown to control in a very direct way the multifractal spectrum and the correlation structure of the increments. We briefly explain how, in the same way, one can build stationary multifractal processes or positive random measures.

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