Relaxation problem with quadratic noise
type: Item
instance of: scholarly article
title: Relaxation problem with quadratic noise
zbMATH Open document ID: 0652.60063
DOI: 10.1007/BF01033093
published in: Journal of Statistical Physics
publication date: 1986-01-01T00:00:00Z
review text: A linear first-order equation with a quadratic colored noise is considered. An exact one-dimensional probability distribution of the process is obtained from the characteristic function. The characteristic function is calculated by means of special functionals of the noise. An auxiliary set of three ordinary differential equations (which contains a Riccati equation) is solved for all values of parameters of the problem. In peculiar cases, the characteristic function is expressed by elementary functions. Graphs of the probability density function are presented for a few cases. The article is a continuation of the author's previous paper, Exact probability distribution for soluble model with quadratic noise, ibid. 42, 1009-1018 (1986).
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 34F05
zbMATH DE Number: 4064183
zbMATH Keywords: Langevin equation
zbMATH Keywords: relaxation problem
zbMATH Keywords: characteristic function
zbMATH Keywords: Riccati equation
author: Jerzy Łuczka
MaRDI profile type: Publication
cites work: Q5518575
full work available at URL: https://doi.org/10.1007/bf01033093
OpenAlex ID: W1994385484
description: scientific article; zbMATH DE number 4064183