  Holographic model of massive scalar field with its self-interaction
$\lambda\phi^n$ in AdS space is able to give a logarithmic scale dependence to
marginal multi trace deformation couplings on its dual conformal field theory,
where $\lambda$ is the self-interaction coupling of the scalar field, $\phi$
and $n$ is an integral number. In arXiv:1501.06664, the authors realize this
feature by looking at bulk scalar solutions near AdS boundary imposing a
specific boundary condition between the coefficients of non-normalizable and
normalizable modes of the scalar field excitations. We study the same
holographic model to see scale dependence of marginal deformations on the dual
conformal field theory by employing completely different method: {\it
holographic Wilsonian renormalization group}. We solve Hamilton-Jacobi equation
derived from the holographic model of massive scalar with $\lambda\phi^n$
interaction and obtain the solution of marginal multi trace deformations up to
the leading order in $\lambda$. It turns out that the solution of marginal
multi trace deformation also presents logarithmic behavior in energy scale near
UV region.
