Frontiers of Mathematics in China >

0 317 - 343

DOI: https://doi.org/10.1007/s11464-013-0229-6

RESEARCH ARTICLE

Mixed principal eigenvalues in dimension one

  • Mu-Fa CHEN ,
  • Lingdi WANG ,
  • Yuhui ZHANG
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  • School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems (Beijing Normal University), Ministry of Education, Beijing 100875, China

Received date: 06 Mar 2012

Accepted date: 08 Jun 2012

Published date: 01 Apr 2013

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg
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Abstract

This is one of a series of papers exploring the stability speed of one-dimensional stochastic processes. The present paper emphasizes on the principal eigenvalues of elliptic operators. The eigenvalue is just the best constant in the L2-Poincaré inequality and describes the decay rate of the corresponding diffusion process. We present some variational formulas for the mixed principal eigenvalues of the operators. As applications of these formulas, we obtain case by case explicit estimates, a criterion for positivity, and an approximating procedure for the eigenvalue.

Key words： Eigenvalue; variational formula; explicit estimate; positivity criterion; approximating procedure

Cite this article

Mu-Fa CHEN , Lingdi WANG , Yuhui ZHANG . Mixed principal eigenvalues in dimension one[J]. Frontiers of Mathematics in China, 0 , 8(2) : 317 -343 . DOI: 10.1007/s11464-013-0229-6

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