Limit theorems for stochastic recursions with Markov dependent coefficients
Volume 128 / 2012
Colloquium Mathematicum 128 (2012), 263-276
MSC: 60F05, 60J05.
DOI: 10.4064/cm128-2-12
Abstract
We consider the stochastic recursion $X_n = A_n X_{n-1}+ B_n$ for Markov dependent coefficients $(A_n,B_n)\in\mathbb R^+\times\mathbb R$. We prove the central limit theorem, the local limit theorem and the renewal theorem for the partial sums $S_n = X_1+\cdots + X_n$.
