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On the factor ordering problem in stochastic inflation
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The stochastic approach to inflation suffers from ambiguities due to the arbitrary choice of the time variable and due to the choice of the factor ordering in the corresponding Fokker-Planck equation. Here it is shown that both ambiguities can be removed if we require that the factor ordering should be set in such a way that physical results are invariant with respect to time reparametrizations. This requirement uniquely selects the so-called Ito factor ordering. Additional ambiguities associated with non-trivial kinetic terms of the scalar fields are also discussed, as well as ways of constraining these ambiguities.
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It\^{o}, Stratonovich, and zoom-in schemes in stochastic inflation
An alternating drift-and-kick 'zoom-in' scheme for stochastic inflation is equivalent to the Itô interpretation, and the Itô-Stratonovich difference vanishes in the full non-Markovian setup.
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