From shape to randomness: A classification of Langevin stochasticity

Iddo Eliazar, Morrel H. Cohen

Research output: Contribution to journalArticle

9 Scopus citations

Abstract

The Langevin equation-perhaps the most elemental stochastic differential equation in the physical sciences-describes the dynamics of a random motion driven simultaneously by a deterministic potential field and by a stochastic white noise. The Langevin equation is, in effect, a mechanism that maps the stochastic white-noise input to a stochastic output: a stationary steady state distribution in the case of potential wells, and a transient extremum distribution in the case of potential gradients. In this paper we explore the degree of randomness of the Langevin equation's stochastic output, and classify it à la Mandelbrot into five states of randomness ranging from "infra-mild" to "ultra-wild". We establish closed-form and highly implementable analytic results that determine the randomness of the Langevin equation's stochastic output-based on the shape of the Langevin equation's potential field.

Original languageEnglish (US)
Pages (from-to)27-42
Number of pages16
JournalPhysica A: Statistical Mechanics and its Applications
Volume392
Issue number1
DOIs
StatePublished - Jan 1 2013

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Condensed Matter Physics

Keywords

  • Geometric Langevin dynamics
  • Langevin dynamics
  • Mild randomness
  • Potential gradients
  • Potential wells
  • Stochastic equilibria
  • Stochastic extrema
  • Wild randomness

Fingerprint Dive into the research topics of 'From shape to randomness: A classification of Langevin stochasticity'. Together they form a unique fingerprint.

  • Cite this