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In probability theory, lumpability is a method for reducing the size of the state space of some continuous-time Markov chains, first published by Kemeny and Snell.〔 〕 ==Definition== Suppose that the complete state-space of a Markov chain is divided into disjoint subsets of states, where these subsets are denoted by ''ti''. This forms a partition is lumpable with respect to the partition ''T'' if and only if, for any subsets ''ti'' and ''tj'' in the partition, and for any states ''n,n’'' in subset ''ti'', : where ''q''(''i,j'') is the transition rate from state ''i'' to state ''j''.〔Jane Hillston, (''Compositional Markovian Modelling Using A Process Algebra'' ) in the Proceedings of the Second International Workshop on Numerical Solution of Markov Chains: Computations with Markov Chains, Raleigh, North Carolina, January 1995. Kluwer Academic Press〕 Similarly, for a stochastic matrix ''P'', ''P'' is a lumpable matrix on a partition ''T'' if and only if, for any subsets ''ti'' and ''tj'' in the partition, and for any states ''n,n’'' in subset ''ti'', : where ''p''(''i,j'') is the probability of moving from state ''i'' to state ''j''.〔Peter G. Harrison and Naresh M. Patel, ''Performance Modelling of Communication Networks and Computer Architectures'' Addison-Wesley 1992〕 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「lumpability」の詳細全文を読む スポンサード リンク
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