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We develop a method for treating a series of secularly growing terms obtainedfrom quantum perturbative calculations: autonomous first-order differentialequations are constructed such that they reproduce this series to the givenorder. The exact solutions of these equations are free of secular terms andapproach a finite limit at late times. This technique is illustrated for thewell-known problem of secular growth of correlation functions of a masslessscalar field with a quartic self-interaction in de Sitter space. For theexpectation value of the product of two fields at coinciding space-time pointswe obtain a finite late-time result that is very close to the one followingfrom Starobinsky's stochastic approach.

Renormalization group inspired autonomous equations for secular effects in de Sitter space