Limit theorems for stochastic recursions with Markov dependent coefficients
Colloquium Mathematicum, Tome 128 (2012) no. 2, pp. 263-276
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences
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 $S_n = X_1+\cdots + X_n$.
Keywords:
consider stochastic recursion n markov dependent coefficients n mathbb times mathbb prove central limit theorem local limit theorem renewal theorem partial sums cdots
Affiliations des auteurs :
Dariusz Buraczewski 1 ; Małgorzata Letachowicz 2
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author = {Dariusz Buraczewski and Ma{\l}gorzata Letachowicz},
title = {Limit theorems for stochastic recursions with {Markov} dependent coefficients},
journal = {Colloquium Mathematicum},
pages = {263--276},
year = {2012},
volume = {128},
number = {2},
doi = {10.4064/cm128-2-12},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/cm128-2-12/}
}
TY - JOUR AU - Dariusz Buraczewski AU - Małgorzata Letachowicz TI - Limit theorems for stochastic recursions with Markov dependent coefficients JO - Colloquium Mathematicum PY - 2012 SP - 263 EP - 276 VL - 128 IS - 2 UR - http://geodesic.mathdoc.fr/articles/10.4064/cm128-2-12/ DO - 10.4064/cm128-2-12 LA - en ID - 10_4064_cm128_2_12 ER -
%0 Journal Article %A Dariusz Buraczewski %A Małgorzata Letachowicz %T Limit theorems for stochastic recursions with Markov dependent coefficients %J Colloquium Mathematicum %D 2012 %P 263-276 %V 128 %N 2 %U http://geodesic.mathdoc.fr/articles/10.4064/cm128-2-12/ %R 10.4064/cm128-2-12 %G en %F 10_4064_cm128_2_12
Dariusz Buraczewski; Małgorzata Letachowicz. Limit theorems for stochastic recursions with Markov dependent coefficients. Colloquium Mathematicum, Tome 128 (2012) no. 2, pp. 263-276. doi: 10.4064/cm128-2-12
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