Stretched exponential in non-linear stochastic field theories

We consider the time dependent two point function 〈φq(t)φ−q(0)〉 in non-linear stochastic field theories, for which the KPZ equation serves as a prototype, in particular we consider small q's and long times such that ωqt⪢1 (ωq being the corresponding decay rate). We find that, since the generic case has ωq∝qμ for small q where μ>1, the decay of the two point function is given by a stretched exponential in ωqt multiplied by a power of t, 〈φ−q(0)φq(t)〉∝tβdexp[−γ(ωqt)1/μ], where βd=(d−1)/2μ, d is the dimensionality of space and γ a dimensionless constant.