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In the mathematical study of stochastic processes, a Harris chain is a Markov chain where the chain returns to a particular part of the state space an unbounded number of times. Harris chains are regenerative processes and are named after Theodore Harris. ==Definition== A Markov chain on state space Ω with stochastic kernel ''K'' is a ''Harris chain''〔R. Durrett. ''Probability: Theory and Examples''. Thomson, 2005. ISBN 0-534-42441-4.〕 if there exist ''A'', ''B'' ⊆ Ω, ϵ > 0, and probability measure ρ with ρ(''B'') = 1 such that # If τ''A'' := inf , then P(τ''A'' < ∞ | ''X''0 = ''x'') > 0 for all ''x'' ∈ Ω. # If ''x'' ∈ ''A'' and ''C'' ⊆ ''B'' then ''K''(''x'', ''C'') ≥ ''ερ''(''C''). In essence, this technical definition can be rephrased as follows: given two points ''x''1 and ''x''2 in ''A'', then there is at least an ϵ chance that they can be moved together to the same point at the next time step. Another way to say it is that suppose that ''x'' and ''y'' are in ''A''. Then at the next time step I first flip a Bernoulli with parameter ϵ. If it comes up one, I move the points to a point chosen using ρ. If it comes up zero, the points move independently, with ''x'' moving according to P(''X''''n''+1 ∈ C | ''Xn'' = ''x'') = ''K''(''x'', ''C'') − ''ερ''(''C'') and ''y'' moving according to P(''Y''''n''+1 ∈ ''C'' | ''Y''''n'' = ''y'') = . 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Harris chain」の詳細全文を読む スポンサード リンク
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