СтаттяЗовнішня публікація1 лютого 2026 р.

Stochastic self-similarity and stationarity: Novel perspectives for heterogeneous and multifractal processes

Hubert WoszczekORCIDAgnieszka WyłomańskaSamudrajit ThapaORCIDAleksei V. ChechkinORCID

Анотація

We introduce novel perspectives on stochastic self-similarity and stationarity, addressing limitations and extensions of classical definitions when applied to heterogeneous and multifractal processes. We propose a new notion of stochastic self-similarity encompassing processes with random parameters and establish a corresponding Lamperti transformation. The concept of stationarity in marginal distributions is introduced and connected with self-similarity in marginal distributions, particularly relevant for processes with time-dependent Hurst exponent. Our results provide a comprehensive overview of definitions of self-similarity and stationarity accompanied by illustrative examples and explore relationships between the different notions through Lamperti transformations.

Класифікація

Домен

Physical SciencesSocial Sciences

Галузь

Physics and AstronomyEconomics, Econometrics and Finance

Підгалузь

Statistical and Nonlinear PhysicsEconomics and Econometrics

Тема

Statistical Mechanics and EntropyChaos control and synchronization★Complex Systems and Time Series Analysis

Ідентифікатори

DOI: 10.1063/5.0303279

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