Wiener-Khinchin Theorem for Nonstationary Scale-Invariant Processes

Andreas Dechant, Eric Lutz

Research output: Contribution to journalArticlepeer-review

24 Citations (Scopus)


We derive a generalization of the Wiener-Khinchin theorem for nonstationary processes by introducing a time-dependent spectral density that is related to the time-averaged power. We use the nonstationary theorem to investigate aging processes with asymptotically scale-invariant correlation functions. As an application, we analyze the power spectrum of three paradigmatic models of anomalous diffusion: scaled Brownian motion, fractional Brownian motion, and diffusion in a logarithmic potential. We moreover elucidate how the nonstationarity of generic subdiffusive processes is related to the infrared catastrophe of 1/f noise.

Original languageEnglish
Article number080603
JournalPhysical review letters
Issue number8
Publication statusPublished - 2015 Aug 18
Externally publishedYes

ASJC Scopus subject areas

  • Physics and Astronomy(all)


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