  The statistical linearization method known in nonlinear mechanics and random
vibrations theory has been applied to stochastically quantized fields in finite
temperature. It has been shown that even in its simplest form the method yields
convenient implicit equations for the self-energy, equivalent to the
Dyson-Schwinger equations resulting from the summation of infinite number of
perturbative diagrams. Three examples have been provided: the quantum
anharmonic oscillator, the scalar $\phi^{4}$ theory in three spatial dimension,
and the Bose-Hubbard model. The Ramanujan summation has been used to deal with
divergent integrals and series.
