  We propose a $1/N$ expansion of Starobinsky and Yokoyama's effective
stochastic approach for light quantum fields on superhorizon scales in de
Sitter spacetime. We explicitly compute the spectrum and the eigenfunctions of
the Fokker-Planck operator for a O($N$)-symmetric theory with quartic
selfinteraction at leading and next-to-leading orders in this expansion. We
obtain simple analytical expressions valid in various nonperturbative regimes
in terms of the interaction coupling constant.
