Periodic linear discrete multitime diagonal recurrence with application in economics

Abstract

Floquet theory, first published in 1883 for periodic linear differential equations, is extended in this paper to multitime diagonal recurrences. We find explicitly a monodromy matrix, and we comment its eigenvalues (called Floquet multipliers). The Floquet point of view brings about an important simplification: the initial linear diagonal recurrence system is reduced to a linear recurrence system, with constant coefficients along "diagonal lines". The results are applied to the discrete multitime Samuelson-Hicks models, with constant, respectively multi-periodic, coefficients, in order to find bivariate sequences with economic meaning. For constant coefficients case, it was found also the generating function; for multi-periodic coefficients case, we determined the Floquet multipliers.