From shape to randomness: A classification of Langevin stochasticity
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.
Volume (Year): 392 (2013)
Issue (Month): 1 ()
|Contact details of provider:|| Web page: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/|
When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:392:y:2013:i:1:p:27-42. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei)
If references are entirely missing, you can add them using this form.