Correlation effects for stochastic zeros of Sturm-Liouville equations
type: Item
instance of: scholarly article
title: Correlation effects for stochastic zeros of Sturm-Liouville equations
zbMATH Open document ID: 0693.34019
published in: Hiroshima Mathematical Journal
publication date: 1988-01-01T00:00:00Z
review text: Consider the stochastic Sturm-Liouville equations of the form \[ (1)\quad (p(x,\omega)u')'+q(x,\omega)u=0,\quad (x,\omega)\in [0,\infty)\times \Omega,\quad u(0,\omega)=0 \] with probability 1, and the most obvious deterministic approximation to such, the classical Sturm-Liouville equation \[ (2)\quad (P(x)v')'+Q(x)v=0,\quad x\in [0,\infty),\quad v(0)=0, \] where P and Q are the expected values of p and q relative to a given probability space \(\Omega\). Denote the smallest positive zeros of such solutions of (1) and (2) by \(\xi\) (\(\omega)\) and \(\eta\), respectively, and by X the expected value of \(\xi\) (\(\omega)\) relative to \(\Omega\). The paper focuses on the nature of the correlation between p and q in establishing criteria for \(X\geq \eta\).
reviewed by: C.Simirad
Mathematics Subject Classification ID: 34L99
Mathematics Subject Classification ID: 34F05
zbMATH DE Number: 4134466
zbMATH Keywords: stochastic Sturm-Liouville equations
author: Kurt Kreith
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.32917/hmj/1206129617
OpenAlex ID: W1528211911
Wikidata QID: Q128871219
DOI: 10.32917/HMJ/1206129617
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description: scientific article; zbMATH DE number 4134466