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Mixed principal eigenvalues in dimension one
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.Comment: 45 pages; Front. Math. China, 201
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