AR(1) sequence with random coefficients: Regenerative properties and its application

Krishna B. Athreya, Koushik Saha, Radhendushka Srivastava

Let $\{X_n{\}}_{n\ge 0}$ be a sequence of real valued random variables such that $X_n={\rho }_n{X}_{n-1}+{\epsilon }_n,n=1,2,\dots$, where $\{({\rho }_n,{\epsilon }_n){\}}_{n\ge 1}$ are i.i.d. and independent of initi…