Editing Pink noise (section)

=== Diffusion processes ===
Many time-dependent stochastic processes are known to exhibit 1/''f''<sup>&nbsp;α</sup> noises with α between 0 and 2. In particular [[Brownian motion]] has a [[Spectral density|power spectral density]] that equals 4''D''/''f''<sup>&nbsp;2</sup>,<ref>{{Cite book|title=Fundamentals of noise and vibration analysis for engineers|last=Norton, M. P. |date=2003|publisher=Cambridge University Press|others=Karczub, D. G. (Denis G.)|isbn=9780511674983|edition= 2nd|location=Cambridge, UK|oclc=667085096}}</ref> where ''D'' is the [[Mass diffusivity|diffusion coefficient]]. This type of spectrum is sometimes referred to as [[Brownian noise]]. The analysis of individual Brownian motion trajectories also show 1/''f''<sup>&nbsp;2</sup> spectrum, albeit with random amplitudes.<ref>{{Cite journal|last1=Krapf|first1=Diego|last2=Marinari|first2=Enzo|last3=Metzler|first3=Ralf|last4=Oshanin|first4=Gleb|last5=Xu|first5=Xinran|last6=Squarcini|first6=Alessio|date=2018-02-09|title=Power spectral density of a single Brownian trajectory: what one can and cannot learn from it|journal=New Journal of Physics|volume=20|issue=2|pages=023029|doi=10.1088/1367-2630/aaa67c|arxiv=1801.02986|bibcode=2018NJPh...20b3029K|issn=1367-2630|doi-access=free}}</ref> [[Fractional Brownian motion]] with [[Hurst exponent]] ''H'' also show 1/''f''<sup>&nbsp;α</sup> power spectral density with α=2''H''+1 for subdiffusive processes (''H''<0.5) and α=2 for superdiffusive processes (0.5<''H''<1).<ref>{{Cite journal|last1=Krapf|first1=Diego|last2=Lukat|first2=Nils|last3=Marinari|first3=Enzo|last4=Metzler|first4=Ralf|last5=Oshanin|first5=Gleb|last6=Selhuber-Unkel|first6=Christine|last7=Squarcini|first7=Alessio|last8=Stadler|first8=Lorenz|last9=Weiss|first9=Matthias|last10=Xu|first10=Xinran|date=2019-01-31|title=Spectral Content of a Single Non-Brownian Trajectory|journal=Physical Review X|language=en|volume=9|issue=1|pages=011019|doi=10.1103/PhysRevX.9.011019| arxiv=1902.00481 |bibcode=2019PhRvX...9a1019K|issn=2160-3308|doi-access=free}}</ref>