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Eigentime Identity for One-Dimensional Diffusion Processes

Part of: Markov processes General theory of linear operators

Published online by Cambridge University Press:  30 January 2018

Li-Juan Cheng  and
Yong-Hua Mao
Li-Juan Cheng*
Affiliation:
Zhejiang University of Technology and Beijing Normal University
Yong-Hua Mao*
Affiliation:
Beijing Normal University
*
∗ Postal address: Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou 310023, China.
∗ Postal address: Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou 310023, China.
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Abstract

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The eigentime identity for one-dimensional diffusion processes on the halfline with an entrance boundary at ∞ is obtained by using the trace of the deviation kernel. For the case of an exit boundary at ∞, a similar eigentime identity is presented with the aid of the Green function. Explicit equivalent statements are also listed in terms of the strong ergodicity or the uniform decay for diffusion processes.

Keywords

Hitting timelifetimeeigentime identitystrong ergodicityuniform decayeigenvalue

MSC classification

Primary: 60J60: Diffusion processes 47A75: Eigenvalue problems
Type
Research Article
Information
Journal of Applied Probability , Volume 52 , Issue 1 , March 2015 , pp. 224 - 237
Copyright
© Applied Probability Trust 

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