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Multifractal processes: Definition, properties and new examples

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  • Grahovac, Danijel

Abstract

We investigate stochastic processes possessing scale invariance properties which we refer to as multifractal processes. The examples of such processes known so far do not go much beyond the original cascade construction of Mandelbrot. We provide a new definition of the multifractal process by generalizing the definition of the self-similar process. We establish general properties of these processes and show how existing examples fit into our setting. Finally, we define a new class of examples inspired by the idea of Lamperti transformation. Namely, for any pair of infinitely divisible distribution and a stationary process one can construct a multifractal process.

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  • Grahovac, Danijel, 2020. "Multifractal processes: Definition, properties and new examples," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    • Handle: RePEc:eee:chsofr:v:134:y:2020:i:c:s0960077920301375
    DOI: 10.1016/j.chaos.2020.109735
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    1. Saâdaoui, Foued, 2024. "Segmented multifractal detrended fluctuation analysis for assessing inefficiency in North African stock markets," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).

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