Limit theorems for stochastic recursions with Markov dependent coefficients

Dariusz Buraczewski¹ ; Małgorzata Letachowicz²

¹ Instytut Matematyczny Uniwersytet Wrocławski pl. Grunwaldzki 2/4 50-384 Wrocław, Poland
² Politechnika Opolska Mikołajczyka 5 45-271 Opole, Poland

Colloquium Mathematicum, Tome 128 (2012) no. 2, pp. 263-276.

Résumé

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 $S_n=X_1+\cdots +X_n$.

Détail

DOI : 10.4064/cm128-2-12

Mots-clés : consider stochastic recursion n markov dependent coefficients n mathbb times mathbb prove central limit theorem local limit theorem renewal theorem partial sums cdots