The misconception of mean-reversion

Iddo I. Eliazar, Morrel H. Cohen

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


The notion of random motion in a potential well is elemental in the physical sciences and beyond. Quantitatively, this notion is described by reverting diffusions - asymptotically stationary diffusion processes which are simultaneously (i) driven toward a reversion level by a deterministic force, and (ii) perturbed off the reversion level by a random white noise. The archetypal example of reverting diffusions is the Ornstein-Uhlenbeck process, which is mean-reverting. In this paper we analyze reverting diffusions and establish that: (i) if the magnitude of the perturbing noise is constant then the diffusion's stationary density is unimodal and the diffusion is mode-reverting; (ii) if the magnitude of the perturbing noise is non-constant then, in general, neither is the diffusion's stationary density unimodal, nor is the diffusion mode-reverting. In the latter case we further establish a result asserting when unimodality and mode-reversion do hold. In particular, we demonstrate that the notion of mean-reversion, which is fundamental in economics and finance, is a misconception - as mean-reversion is an exception rather than the norm.

Original languageEnglish (US)
Article number332001
JournalJournal of Physics A: Mathematical and Theoretical
Issue number33
StatePublished - Aug 24 2012

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modeling and Simulation
  • Mathematical Physics
  • General Physics and Astronomy


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