The conventional truncation in stochastic inflation is inconsistent because quadratic-noise contributions are the same perturbative order as the deterministic non-Markovian corrections.
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Stochastic effects in multifield inflation make the number of fields relevant for e-fold statistics and power spectrum, with a general formula for higher moments and an upper bound on fields for successful inflation.
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A consistent formulation of stochastic inflation I: Non-Markovian effects and issues beyond linear perturbations
The conventional truncation in stochastic inflation is inconsistent because quadratic-noise contributions are the same perturbative order as the deterministic non-Markovian corrections.
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Multifield stochastic inflation: Relevance of number of fields in statistical moments
Stochastic effects in multifield inflation make the number of fields relevant for e-fold statistics and power spectrum, with a general formula for higher moments and an upper bound on fields for successful inflation.