  In this study, we formulate a systematic way of deriving an effective
equation of motion(EoM) for long wavelength modes of a massless scalar field
with a general potential $V(\phi)$ on de Sitter background, and investigate
whether or not the effective EoM can be described as a classical stochastic
process. Our formulation gives an extension of the usual stochastic formalism
to including sub-leading secular growth coming from the nonlinearity of short
wavelength modes. Applying our formalism to $\lambda \phi^4$ theory, we
explicitly derive an effective EoM which correctly recovers the next-to-leading
secularly growing part at a late time, and show that this effective EoM can be
seen as a classical stochastic process. Our extended stochastic formalism can
describe all secularly growing terms which appear in all correlation functions
with a specific operator ordering, which will not be a big drawback because the
commutator of a light scalar field becomes negligible at large scales owing to
the squeezing.
