  This paper is concerned with classes of models of stochastic reaction
dynamics with time-scales separation. We demonstrate that the existence of the
time-scale separation naturally leads to the application of the averaging
principle and elimination of degrees of freedom via the renormalization of
transition rates of slow reactions. The method suggested in this work is more
general than other approaches presented previously: it is not limited to a
particular type of stochastic processes and can be applied to different types
of processes describing fast dynamics, and also provides crossover to the case
when separation of time scales is not well pronounced. We derive a family of
exact fluctuation-dissipation relations which establish the connection between
effective rates and the statistics of the reaction events in fast reaction
channels. An illustration of the technique is provided. Examples show that
renormalized transition rates exhibit in general non-exponential relaxation
behavior with a broad range of possible scenarios.
