  To determine the effect of nonradiative excitation energy transfer on the
fluorescence of a rigid multicomponent solution, a new analytical method was
developed by treating this transfer as a time-resolved Markov chain (TRMC). In
the TRMC approach, we assume that the Markov chain under consideration is
governed by bivariate joint probability mass-density functions. One of the
random variables is discrete and represents the state number to which the
process passes at a given step, while the other random variable is continuous
and determines the moment in time at which this transition occurs. In general,
the time distributions of this second variable can be arbitrary, continuous or
discrete, and not just exponential, as required by the method known as
continuous time Markov chains (CTMC). The correctness of the TRMC method is
confirmed by the fact that the time courses of fluorescence intensities
calculated by this method agree with those calculated using ordinary analytical
methods. In the section on calculating the quantum yields of individual
components, the suitability of a method known as discrete time Markov chains
(DTMC) was found. However, we argue that the DTMC method does not refer to time
and propose to rename it as time-unspecified Markov chain (TUMC). The results
generated by TRMC, when integrated over time, become equivalent to those
generated by TUMC. The fluorescence cases of binary and ternary solutions are
discussed in detail
