Discrete linear multiple recurrence with multi-periodic coefficients

TL;DR

This paper develops a Floquet theory approach for solving linear multiple periodic recurrence equations, simplifying their analysis and applying results to economic multitime models with periodic coefficients.

Contribution

It introduces a Floquet-based framework for linear multiple recurrence systems with periodic coefficients, including explicit fundamental and monodromy matrices.

Findings

Explicit form of the fundamental matrix and monodromy matrix provided

Eigenvalues (Floquet multipliers) characterized for these systems

Application to economic multitime Samuelson-Hicks models with periodic coefficients

Abstract

The aim of our paper is to formulate and solve problems concerning linear multiple periodic recurrence equations. Among other things, we discuss in detail the cases with periodic and multi-periodic coefficients, highlighting in particular the theorems of Floquet type. For this aim, we find specific forms for the fundamental matrix. Explicitly monodromy matrix is given, and its eigenvalues (called Floquet multipliers) are shown. The Floquet point of view brings about an important simplification: the initial linear multiple recurrence system is reduced to another linear multiple recurrence system, with constant coefficients along partial directions. 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.