In the preceding paper (Boguna et al., Physica A 282 (2000) 475), we develo
ped formalism to calculate a probability density for the cumulative time sp
ent in one out of a two-state non-Markovian system of the form S-1 reversib
le arrow S-2 when the system is observed continuously for a time T. The asy
mptotic 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 reversible arrow S-2 reversible arrow...reversible arrow S-N to an equ
ivalent two-state system. This also shows that the probability density for
the cumulative residence time in a single state is asymptotic to a Gaussian
. (C) 2000 Elsevier Science B.V. All rights reserved.