  This paper aims at using the functional renormalization group formalism to
study the equilibrium states of a stochastic process described by a
quench--disordered multilinear Langevin equation. Such an equation
characterizes the evolution of a time-dependent $N$-vector
$q(t)=\{q_1(t),\cdots q_N(t)\}$ and is traditionally encountered in the
dynamical description of glassy systems at and out of equilibrium through the
so-called Glauber model. From the connection between Langevin dynamics and
quantum mechanics in imaginary time, we are able to coarse-grain the path
integral of the problem in the Fourier modes, and to construct a
renormalization group flow for effective Euclidean action. In the large
$N$-limit we are able to solve the flow equations for both matrix and tensor
disorder. The numerical solutions of the resulting exact flow equations are
then investigated using standard local potential approximation, taking into
account the quench disorder. In the case where the interaction is taken to be
matricial, for finite $N$ the flow equations are also solved. However, the case
of finite $N$ and taking into account the non-equilibrum process will be
considered in a companion investigation.
