Renormalization scheme and higher loop stability in hadronic tau decay within analytic perturbation theory

We apply an analytic description to the inclusive decay of the tau lepton. We argue that this method gives not only a self-consistent description of t he process both in the timelike region by using the initial expression for R-tau and in the spacelike domain by using the analytic properties of the h adronic correlator, but also leads to the fact that theoretical uncertainti es associated with unknown higher-loop contributions and renormalization sc heme dependence can be reduced dramatically.