  Interacting quantum scalar field theories in $dS_D\times M_d$ spacetime can
be reduced to Euclidean field theories in $M_d$ space in the vicinity of $I_+$
infinity of $dS_D$ spacetime. Using this non-perturbative mapping, we analyze
the critical behavior of Euclidean $\lambda\phi_4^4$ theory in the symmetric
phase and find the asymptotic behavior $\beta(\lambda)\sim \lambda$ of the beta
function at strong coupling. Scaling violating contributions to the beta
function are also estimated in this regime.
