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This paper is concerned with classes of models of stochastic reactiondynamics with time-scales separation. We demonstrate that the existence of thetime-scale separation naturally leads to the application of the averagingprinciple and elimination of degrees of freedom via the renormalization oftransition rates of slow reactions. The method suggested in this work is moregeneral than other approaches presented previously: it is not limited to aparticular type of stochastic processes and can be applied to different typesof processes describing fast dynamics, and also provides crossover to the casewhen separation of time scales is not well pronounced. We derive a family ofexact fluctuation-dissipation relations which establish the connection betweeneffective rates and the statistics of the reaction events in fast reactionchannels. An illustration of the technique is provided. Examples show thatrenormalized transition rates exhibit in general non-exponential relaxationbehavior with a broad range of possible scenarios.

Averaging Methods for Stochastic Dynamics of Complex Reaction Networks: Description of Multiscale Couplings