文章基本信息

标题：Metastability of finite state Markov chains: a recursive procedure to identify slow variables for model reduction
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作者：Claudio Landim ; Tiecheng Xu
期刊名称：Latin American Journal of Probability and Mathematical Statistics
电子版ISSN：1980-0436
出版年度：2016
卷号：XIII
期号：2
页码：725-751
出版社：Instituto Nacional De Matemática Pura E Aplicada
摘要：Consider a sequence (ηN(t) : t ≥ 0) of continuous-time, irreducibleMarkov chains evolving on a fixed finite set E. Denote by RN(η, ξ) the jumprates of the Markov chain ηNt , and assume that for any pair of bonds (η, ξ), (η′, ξ′)arctan{RN(η, ξ)/RN(η′, ξ′)} converges as N ↑ ∞. Under a hypothesis slightlymore restrictive (cf. (2.6) below), we present a recursive procedure which providesa sequence of increasing time-scales θ1N, . . . , θpN, θjN ≪ θj+1N , and of coarseningpartitions of the set E, {Ej1, . . . , Ejnj ,j}, 1 ≤ j ≤ p, with the following property.Let φj : E → {0, 1, . . . , nj} be the projection defined by φj (η) =Pnjx=1 x 1{η ∈ Ejx}.For each 1 ≤ j ≤ p, we prove that the hidden Markov chain XjN(t) = φj(ηN(tθjN))converges to a Markov chain on {1, . . . , nj}.
关键词：Metastability; Markov chains; slow variables; model reduction.