fundamental theorem of demography

Let At be a sequence of n×n nonnegative primitive matrices. Suppose that AtA, with A also a nonnegative primitive matrix. Define the sequence xt+1=Atxt, with xtn. If x00, then


where p is the normalized (p=1) eigenvectorMathworldPlanetmathPlanetmathPlanetmath associated to the eigenvalueMathworldPlanetmathPlanetmathPlanetmathPlanetmath of A (also called the Perron-Frobenius eigenvector of A).

Title fundamental theorem of demography
Canonical name FundamentalTheoremOfDemography
Date of creation 2013-03-22 13:18:28
Last modified on 2013-03-22 13:18:28
Owner jarino (552)
Last modified by jarino (552)
Numerical id 6
Author jarino (552)
Entry type Theorem
Classification msc 37A30
Classification msc 92D25
Synonym a weak ergodic theorem
Related topic PerronFrobeniusTheorem