Mixed principal eigenvalues in dimension one

This is one of a series of papers exploring the stability speed of one-dimensional stochastic processes. The present paper emphasizes on the principal eigenvalues of elliptic operators. The eigenvalue is just the best constant in the L2-Poincare inequality and describes the decay rate of the corresp...

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Bibliographic Details
Published inFrontiers of Mathematics Vol. 8; no. 2; pp. 317 - 343
Main Authors Chen, Mu-Fa, Wang, Lingdi, Zhang, Yuhui
Format Journal Article
LanguageEnglish
Published Heidelberg SP Higher Education Press 01.04.2013
Springer Nature B.V
Subjects
Approximation
China
Decay rate
Eigenvalues
Estimates
Hypotheses
Inequalities
Mathematical analysis
Mathematical models
Mathematics
Mathematics and Statistics
Operators
Research Article
Stochastic processes
Studies
一维
变分公式
最佳常数
椭圆算子
混合
特征值
稳定速度
随机过程
explicit estimate
60J60
approximating procedure
Eigenvalue
variational formula
34L15
positivity criterion
Online AccessGet full text
ISSN1673-3452
2731-8648
1673-3576
2731-8656
DOI10.1007/s11464-013-0229-6

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Summary:This is one of a series of papers exploring the stability speed of one-dimensional stochastic processes. The present paper emphasizes on the principal eigenvalues of elliptic operators. The eigenvalue is just the best constant in the L2-Poincare inequality and describes the decay rate of the corresponding diffusion process. We present some variational formulas for the mixed principal eigenvalues of the operators. As applications of these formulas, we obtain case by case explicit estimates, a criterion for positivity, and an approximating procedure for the eigenvalue.
Bibliography:Eigenvalue, variational formula, explicit estimate, positivity criterion, approximating procedure
This is one of a series of papers exploring the stability speed of one-dimensional stochastic processes. The present paper emphasizes on the principal eigenvalues of elliptic operators. The eigenvalue is just the best constant in the L2-Poincare inequality and describes the decay rate of the corresponding diffusion process. We present some variational formulas for the mixed principal eigenvalues of the operators. As applications of these formulas, we obtain case by case explicit estimates, a criterion for positivity, and an approximating procedure for the eigenvalue.
11-5739/O1
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ISSN:1673-3452
2731-8648
1673-3576
2731-8656
DOI:10.1007/s11464-013-0229-6