  We study a mathematical relationship between holographic Wilsonian
renormalization group and stochastic quantization framework. We extend the
original proposal given in arXiv:1209.2242 to interacting theories. The
original proposal suggests that fictitious time(or stochastic time) evolution
of stochastic 2-point correlation function will be identical to the radial
evolution of the double trace operator of certain classes of holographic
models, which are free theories in AdS space. We study holographic gravity
models with interactions in AdS space and establish a map between the
holographic renormalization flow of multi-trace operators and stochastic
$n$-point functions. To give precise examples, we extensively study conformally
coupled scalar theory in AdS$_6$. What we have found is that the stochastic
time $t$ dependent 3-point function obtained from Langevin equation with its
Euclidean action being given by $S_E=2I_{os}$ is identical to holographic
renormalization group evolution of holographic triple trace operator as its
energy scale $r$ changes once an identification of $t=r$ is made. $I_{os}$ is
the on-shell action of holographic model of conformally coupled scalar theory
at the AdS boundary. We argue that this can be fully extended to mathematical
relationship between multi point functions and multi trace operators in each
framework.
