Electronic Communications in Probability

First Eigenvalue of One-dimensional Diffusion Processes

Jian Wang

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Abstract

We consider the first Dirichlet eigenvalue of diffusion operators on the half line. A criterion for the equivalence of the first Dirichlet eigenvalue with respect to the maximum domain and that to the minimum domain is presented. We also describle the relationships between the first Dirichlet eigenvalue of transient diffusion operators and the standard Muckenhoupt's conditions for the dual weighted Hardy inequality. Pinsky's result [17] and Chen's variational formulas [8] are reviewed, and both provide the original motivation for this research.

Article information

Source
Electron. Commun. Probab., Volume 14 (2009), paper no. 23, 232-244.

Dates
Accepted: 24 May 2009
First available in Project Euclid: 6 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465234732

Digital Object Identifier
doi:10.1214/ECP.v14-1464

Mathematical Reviews number (MathSciNet)
MR2507752

Zentralblatt MATH identifier
1192.60090

Subjects
Primary: 60J25: Continuous-time Markov processes on general state spaces
Secondary: 60J27: Continuous-time Markov processes on discrete state spaces

Keywords
First Dirichlet eigenvalue Hardy inequality variational formula transience recurrence diffusion operators

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Wang, Jian. First Eigenvalue of One-dimensional Diffusion Processes. Electron. Commun. Probab. 14 (2009), paper no. 23, 232--244. doi:10.1214/ECP.v14-1464. https://projecteuclid.org/euclid.ecp/1465234732


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