First eigenvalue of birth-death processes with killing

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.

Keywords

First eigenvalue / birth-death processes (with killing) / Schrödinger operator with difference form

References

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