From shape to randomness: A classification of Langevin stochasticity

Iddo Eliazar and Morrel H. Cohen

Physica A: Statistical Mechanics and its Applications, 2013, vol. 392, issue 1, 27-42

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.

Keywords: Langevin dynamics; Geometric Langevin dynamics; Potential wells; Potential gradients; Stochastic equilibria; Stochastic extrema; Mild randomness; Wild randomness (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:392:y:2013:i:1:p:27-42

DOI: 10.1016/j.physa.2012.08.009

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