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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Explicit one-loop computation shows the constraint effective potential for scalars in de Sitter is free of infrared problems and supports its use in stochastic Starobinsky-Yokoyama 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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Scalar field effective potentials in de Sitter spacetime
Explicit one-loop computation shows the constraint effective potential for scalars in de Sitter is free of infrared problems and supports its use in stochastic Starobinsky-Yokoyama inflation.