2012/06/22 by Mu-Fa Chen, Chen, Mu-Fa, Ling-Di Wang +4
Computer Science · Economics, Econometrics and Finance · Mathematics · #Advanced Mathematical Modeling in Engineering #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Biology Tumor Growth #Probability (math.PR) #Spectral Theory (math.SP) #Stochastic processes and financial applications #math.CA #math.PR #math.SP
paper · pdf · doi:10.48550/arxiv.1206.5069
45 pages; Front. Math. China, 2012
arxiv created 2012/06/22 · openalex publication_date 2012/06/22 · arxiv updated 2012/06/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.