Multivariate linear recursions with Markov-dependent coefficients

TL;DR

This paper investigates a multivariate linear recursion with Markov-dependent coefficients, demonstrating that its stationary distribution exhibits multivariate regular variation, extending prior results from i.i.d. coefficient cases.

Contribution

It extends the theory of linear recursions by analyzing Markov-dependent coefficients, showing the stationary distribution's regular variation in a broader setting.

Findings

Stationary solution has multivariate regularly varying distribution

Extends previous i.i.d. coefficient results to Markov-dependent case

Provides theoretical foundation for multivariate regular variation in Markov-dependent recursions

Abstract

We study a linear recursion with random Markov-dependent coefficients. In a "regular variation in, regular variation out" setup we show that its stationary solution has a multivariate regularly varying distribution. This extends results previously established for i.i.d. coefficients.