Multifractal processes: Definition, properties and new examples

Danijel Grahovac

Chaos, Solitons & Fractals, 2020, vol. 134, issue C

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.

Keywords: Multifractal processes; Self-similar processes; Scale invariance; Lamperti transformation (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:134:y:2020:i:c:s0960077920301375

DOI: 10.1016/j.chaos.2020.109735

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