Principal eigenvalue characterization connected with stochastic particle motion in a finite interval
type: Item
instance of: scholarly article
title: Principal eigenvalue characterization connected with stochastic particle motion in a finite interval
zbMATH Open document ID: 1026.60111
DOI: 10.1155/S104895330200028X
author: Ahmed Abdullatif Karaballi
author: F. B. M. Belgacem
published in: Journal of Applied Mathematics and Stochastic Analysis
publication date: 2003-10-13T00:00:00Z
review text: Summary: We show that despite their distinction, both the Stratonovich and Itô calculi lead to the same reactive Fokker-Planck equation: \[ {\partial p\over\partial t}-{\partial\over \partial x}\left[ D{\partial p\over \partial x}-b p\right]= \lambda mp, \tag{1} \] describing stochastic dynamics of a particle moving under the influence of an indefinite potential \(m(x,t)\), a drift \(b(x,t)\), and a constant diffusion \(D\). We treat the periodic-parabolic eigenvalue problem (1) for finite domains having absorbing barriers. We show that under conditions required by the maximum principle, the positive principal eigenvalue \(\lambda^*\) (and the negative principal eigenvalue \(\lambda_*)\) is connected to the probability eigendensity function \(p(x,t)\) by a Reileigh-Ritz like formulation. In the process, we establish the manner of effect of the drift and any inducing potential on the size of the principal eigenvalue. We show that the degree of convexity of the potential plays a major role in this regard.
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 65N25
zbMATH DE Number: 1933143
zbMATH Keywords: Fokker-Planck equation
zbMATH Keywords: indefinite potential
zbMATH Keywords: principal eigenvalue
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1933143