Limit theorems for stochastic recursions with Markov dependent coefficients

Volume 128 / 2012

Dariusz Buraczewski, Małgorzata Letachowicz 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 $S_n = X_1+\cdots + X_n$.

Authors

  • Dariusz BuraczewskiInstytut Matematyczny
    Uniwersytet Wrocławski
    pl. Grunwaldzki 2/4
    50-384 Wrocław, Poland
    e-mail
  • Małgorzata LetachowiczPolitechnika Opolska
    Mikołajczyka 5
    45-271 Opole, Poland
    e-mail

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