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We study relation between stochastic quantization and holographic Wilsonianrenormalization group flow. Considering stochastic quantization of the boundaryon-shell actions with the Dirichlet boundary condition for certain $AdS$ bulkgravity theories, we find that the radial flows of double trace deformations inthe boundary effective actions are completely captured by stochastic timeevolution with identification of the $AdS$ radial coordinate `$r$' with thestochastic time '$t$' as $r=t$. More precisely, we investigate Langevindynamics and find an exact relation between radial flow of the double tracecouplings and 2-point correlation functions in stochastic quantization. We alsoshow that the radial evolution of double trace deformations in the boundaryeffective action and the stochastic time evolution of the Fokker-Planck actionare 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$AdS_4$.

Stochastic quantization and holographic Wilsonian renormalization group