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Processes with Long Memory: Regenerative Construction and Perfect Simulation | | Francis Comets
; Roberto Fernandez
; Pablo A. Ferrari
; | | Date: |
22 Sep 2000 | | Subject: | Probability; Statistics; Mathematical Physics MSC-class: 68U20, 60K10, 62J02 | math.PR math-ph math.MP math.ST | | Abstract: | 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. | | Source: | arXiv, math.PR/0009204 | | Services: | Forum | Review | PDF | Favorites | |
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