Limit theorems for stochastic recursions with Markov dependent coefficients

Dariusz Buraczewski, and Małgorzata Letachowicz. "Limit theorems for stochastic recursions with Markov dependent coefficients." Colloquium Mathematicae 128.2 (2012): 263-276. <http://eudml.org/doc/284230>.

@article{DariuszBuraczewski2012,
abstract = {We consider the stochastic recursion $Xₙ = AₙX_\{n-1\} + Bₙ$ for Markov dependent coefficients (Aₙ,Bₙ) ∈ ℝ⁺ × ℝ. We prove the central limit theorem, the local limit theorem and the renewal theorem for the partial sums Sₙ = X₁+ ⋯ + Xₙ.},
author = {Dariusz Buraczewski, Małgorzata Letachowicz},
journal = {Colloquium Mathematicae},
keywords = {stochastic recursion; central limit theorem; local limit theorem; renewal theorem; spectral method},
language = {eng},
number = {2},
pages = {263-276},
title = {Limit theorems for stochastic recursions with Markov dependent coefficients},
url = {http://eudml.org/doc/284230},
volume = {128},
year = {2012},
}

TY - JOUR
AU - Dariusz Buraczewski
AU - Małgorzata Letachowicz
TI - Limit theorems for stochastic recursions with Markov dependent coefficients
JO - Colloquium Mathematicae
PY - 2012
VL - 128
IS - 2
SP - 263
EP - 276
AB - We consider the stochastic recursion $Xₙ = AₙX_{n-1} + Bₙ$ for Markov dependent coefficients (Aₙ,Bₙ) ∈ ℝ⁺ × ℝ. We prove the central limit theorem, the local limit theorem and the renewal theorem for the partial sums Sₙ = X₁+ ⋯ + Xₙ.
LA - eng
KW - stochastic recursion; central limit theorem; local limit theorem; renewal theorem; spectral method
UR - http://eudml.org/doc/284230
ER -