  We study relation between stochastic quantization and holographic Wilsonian
renormalization group flow. Considering stochastic quantization of the boundary
on-shell actions with the Dirichlet boundary condition for certain $AdS$ bulk
gravity theories, we find that the radial flows of double trace deformations in
the boundary effective actions are completely captured by stochastic time
evolution with identification of the $AdS$ radial coordinate `$r$' with the
stochastic time '$t$' as $r=t$. More precisely, we investigate Langevin
dynamics and find an exact relation between radial flow of the double trace
couplings and 2-point correlation functions in stochastic quantization. We also
show that the radial evolution of double trace deformations in the boundary
effective action and the stochastic time evolution of the Fokker-Planck action
are the same. We demonstrate this relation with a couple of examples:
(minimally coupled)massless scalar fields in $AdS_2$ and U(1) vector fields in
$AdS_4$.
