RESEARCH ARTICLE

First eigenvalue of birth-death processes with killing

  • Jian WANG
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  • School of Mathematics and Computer Science, Fujian Normal University, Fuzhou 350007, China

Received date: 04 Jan 2010

Accepted date: 16 Mar 2012

Published date: 01 Jun 2012

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg

Abstract

In this paper, we present an explicit and computable lower bound for the first eigenvalue of birth-death processes with killing. This estimate is qualitatively sharp for birth-death processes without killing. We also establish an approximation procedure for the first eigenvalue of the birth-death process with killing by an increasing principal eigenvalue sequence of some birth-death processes without killing. Some applications of our results are illustrated by many examples.

Cite this article

Jian WANG . First eigenvalue of birth-death processes with killing[J]. Frontiers of Mathematics in China, 2012 , 7(3) : 561 -572 . DOI: 10.1007/s11464-012-0204-7

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