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An effective dynamics of a long wavelength part of an inflation in de Sitter space is derived in the form of the Langevin equation by regarding the remaining short wavelength part as a noise. Classical properties of the noise and the long wavelength part are investigated and their statistical correlations are derived. The formulation is applied to the generation of density perturbations. Here the interaction in the Langevin equation is shown to be indispensable as far as we disregard the singular contribution of the energy-momentum tensor correlation.
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Hosoya et al. (1989) studied this question.
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