New point view of spectral gap in functional spaces for birth-death processes

Abstract

Constructing some proper functional spaces, we obtain the corresponding norm for the operator (-\mathcal{L})^-1, and then, via spectral theory, we revisit two variational formulas of the spectral gap, given by M. F. Chen [Front. Math. China, 2010, 5(3): 379-515], for transient birth-death processes.

Keywords

Birth-death processes / Dirichlet first eigenvalue / variational formula / spectral theory / duality

References

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Higher Education Press and Springer-Verlag Berlin Heidelberg