On limit theorems for functional autoregressive processes with random coefficients

TL;DR

This paper investigates limit theorems for Banach space-valued autoregressive processes with random coefficients, establishing foundational probabilistic results using martingale techniques.

Contribution

It introduces a martingale coboundary decomposition approach to prove limit theorems for these complex processes, extending existing theory.

Findings

Established existence and laws of large numbers for the process

Proved a central limit theorem in Banach space setting

Derived exponential inequalities for the process

Abstract

In this paper, we consider a Banach space valued random coefficient autoregressive process. Our studies on this process involve existence, weak law of large numbers, strong law of large numbers, some exponential inequalities, central limit theorem. Our approach is based on a suitable martingale coboundary decomposition in Banach space.