Frontiers of Mathematics in China >
First eigenvalue of birth-death processes with killing
Received date: 04 Jan 2010
Accepted date: 16 Mar 2012
Published date: 01 Jun 2012
Copyright
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.
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
| 1 |
Chen M F. The principal eigenvalue for jump processes. Acta Math Sin Engl Ser, 2000, 16: 361-368
|
| 2 |
Chen M F. Speed of stability for birth-death processes. Front Math China, 2010, 5: 379-515
|
| 3 |
Chung K L, Zhao Z. From Brownian Motion to Schrödinger’s Equation. Berlin: Springer-Verlag, 1995
|
| 4 |
Davies E B. Spectral Theory and Differential Operators. Cambridge: Cambridge University Press, 1995
|
| 5 |
Reed M, Simon B. Methods of Modern Mathematical Physics. London: Academic Press, 1972
|
| 6 |
Simon B. Functional Integration and Quantum Physics. London: Academic Press, 1979
|
| 7 |
Wang J. First Dirichlet eigenvalue of transient birth-death processes. Preprint, 2008
|
/
| 〈 |
|
〉 |