The Perron-Frobenius Theorem for Markov Semigroups

2014/01/23 by Omar Hijab, Hijab, Omar
Decision Sciences · Computer Science · #Scheduling and Timetabling Solutions #Optimization and Search Problems #Advanced Graph Theory Research

paper · pdf · doi:10.48550/arxiv.1401.5892

Abstract

Let P^V_t, t≥0, be the Schrodinger semigroup associated to a potential V and Markov semigroup P_t, t≥0, on C(X). Existence is established of a left eigenvector and right eigenvector corresponding to the spectral radius e^λ₀t of P^V_t, simultaneously for all t≥0. This is derived with no compactness assumption on the semigroup operators.

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