Mixed principal eigenvalues in dimension one
Probability
2012-06-25 v1 Classical Analysis and ODEs
Spectral Theory
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 -Poincar\'e 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.
Cite
@article{arxiv.1206.5069,
title = {Mixed principal eigenvalues in dimension one},
author = {Mu-Fa Chen and Ling-Di Wang and Yu-Hui Zhang},
journal= {arXiv preprint arXiv:1206.5069},
year = {2012}
}
Comments
45 pages; Front. Math. China, 2012