  The present paper is devoted to the relativistic statistical theory,
introduced in Phys. Rev. E {\bf 66} (2002) 056125 and Phys. Rev. E {\bf 72}
(2005) 036108, predicting the particle distribution function $p(E)=
\exp_{\kappa} (-\beta[E-\mu])$ with $\exp_{\kappa}(x)=(\sqrt{1+ \kappa^2
x^2}+\kappa x)^{1/\kappa}$, and $\kappa^2<1$. This, experimentally observed,
relativistic distribution, at low energies behaves as the exponential,
Maxwell-Boltzmann classical distribution, while at high energies presents power
law tails. Here, we obtain the evolution equation, conducting asymptotically to
the above distribution, by using a new deductive procedure, starting from the
relativistic BBGKY hierarchy and by employing the relativistic molecular chaos
hypothesis.
