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The method is not limited to a particular type of stochastic process and can be applied to different types of processes describing fast dynamics; it 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, nonexponential relaxation behavior with a broad range of possible scenarios.<\/jats:p>","DOI":"10.1137\/050633822","type":"journal-article","created":{"date-parts":[[2006,8,24]],"date-time":"2006-08-24T15:30:24Z","timestamp":1156433424000},"page":"497-513","source":"Crossref","is-referenced-by-count":3,"title":["Averaging Methods for Stochastic Dynamics of Complex Reaction Networks: Description of Multiscale Couplings"],"prefix":"10.1137","volume":"5","author":[{"given":"Sergey","family":"Plyasunov","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Adam P.","family":"Arkin","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,8,3]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1007\/BF00375614"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.94.3.814"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1038\/ng869"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1137\/040603565"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1063\/1.1627296"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1063\/1.481811"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1002\/9780470316658"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1063\/1.1545446"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1063\/1.1505860"},{"key":"R10","doi-asserted-by":"crossref","unstructured":"Y. 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