Processes with Long Memory: Regenerative Construction and Perfect Simulation
概率论
2011-11-10 v3 数学物理
math.MP
统计理论
统计理论
摘要
We present a perfect simulation algorithm for stationary processes indexed by Z, with summable memory decay. Depending on the decay, we construct the process on finite or semi-infinite intervals, explicitly from an i.i.d. uniform sequence. Even though the process has infinite memory, its value at time 0 depends only on a finite, but random, number of these uniform variables. The algorithm is based on a recent regenerative construction of these measures by Ferrari, Maass, Mart{\'\i}nez and Ney. As applications, we discuss the perfect simulation of binary autoregressions and Markov chains on the unit interval.
引用
@article{arxiv.math/0009204,
title = {Processes with Long Memory: Regenerative Construction and Perfect Simulation},
author = {Francis Comets and Roberto Fernandez and Pablo A. Ferrari},
journal= {arXiv preprint arXiv:math/0009204},
year = {2011}
}
备注
27 pages, one figure. Version accepted by Annals of Applied Probability. Small changes with respect to version 2