Discrete multitime multiple recurrence

TL;DR

This paper introduces the theory of multitime multiple recurrence equations, establishing their fundamental properties, existence, and uniqueness of solutions, with applications across various scientific fields.

Contribution

It is the first comprehensive study on multitime multiple recurrences, detailing their properties, solutions, and providing illustrative examples.

Findings

Established existence and uniqueness theorems for solutions.

Analyzed autonomous and non-autonomous cases.

Provided analogues of arithmetic and geometric progressions.

Abstract

The aim of our paper is to formulate and solve problems concerning multitime multiple recurrence equations. We discuss in detail the generic properties and the existence and uniqueness of solutions. Among the general things, we discuss in detail the cases of autonomous and non-autonomous recurrences, highlighting in particular the theorems of existence and uniqueness of solutions. Finally, are given interesting examples which are the analogue of arithmetic progression and the analogue of geometric progression. The multitime multiple recurrences are required in analysis of algorithms, computational biology, information theory, queueing theory, filters theory, statistical physics etc. The theoretical part about them is little or not known, this being the first paper about the subject.