  We explore mathematical relationship between holographic Wilsonian
renormalization group(HWRG) and stochastic quantization(SQ) motivated by the
similarity of the monotonicity in RG flow with Langevin dynamics of
non-equilibrium thermodynamics. We look at scalar field theory in AdS space
with its generic mass, self-interaction, and boundary deformation in the
momentum space. Identifying the stochastic time $t$ with radial coordinate $r$
in AdS, we establish maps between the fictitious time evolution of stochastic
multi point correlation function and the radial evolution of multi-trace
deformation, which respectively, express the relaxation process of Langevin
dynamics and holographic RG flow. We especially consider marginal multi-trace
deformation on the AdS boundary which is successfully captured by a Langevin
dynamics of SQ.
