Mixed principal eigenvalues in dimension one
Received date: 06 Mar 2012
Accepted date: 08 Jun 2012
Published date: 01 Apr 2013
Copyright
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.
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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