Residence time densities for non-Markovian systems. (II). The N-state system

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In the preceding paper (Boguñá et al., Physica A 282 (2000) 475), we developed formalism to calculate a probability density for the cumulative time spent in one out of a two-state non-Markovian system of the form S 1⇄ S 2 when the system is observed continuously for a time T. The asymptotic form for the probability density was shown to be Gaussian. In this paper we indicate how to reduce any reacting nearest-neighbor system, i.e., S 1⇄ S 2⇄⋯⇄ S N to an equivalent two-state system. This also shows that the probability density for the cumulative residence time in a single state is asymptotic to a Gaussian.