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Proceedings of the National Academy of Sciences of the United States of America logoLink to Proceedings of the National Academy of Sciences of the United States of America
. 1975 Mar;72(3):780–783. doi: 10.1073/pnas.72.3.780

On a Variational Formula for the Principal Eigenvalue for Operators with Maximum Principle

Monroe D Donsker 1, S R S Varadhan 1
PMCID: PMC432403  PMID: 16592231

Abstract

In this paper a variational formula is obtained for the principal eigenvalue for operators with maximum principle. This variational formula does not require the operators to be self-adjoint. But if they are self-adjoint this formula reduces to the classical Rayleigh-Ritz formula.

Keywords: semigroups, Rayleigh-Ritz formula, Feynman-Kac formula

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