$\pi^{\pm}, K^{\pm}, p$ and $\overline{p}$ production in $Z^{0} \rightarrow q\overline{q}, Z^{0} \rightarrow b\overline{b}, Z^{0} \rightarrow u\overline{u}, d\overline{d}, s\overline{s}$

The DELPHI experiment at LEP uses Ring Imaging Cherenkov detectors for particle identification. The good understanding of the RICH detectors allows the identification of charged pions, kaons and p rotons, covering the full momentum range from \mbox{$0.7\!<\!p\!<\! 45.6~\gevc$}. The $\pipm$,~$\kapm$, p and $\pbar$ normalised production rates, their differential cross sections, multiplicities a nd the maxima $\xipst$ of the \mbox{$\xip=\ln(1/\xp)$} distributions are measured for three event samples $\zqqbar$, ~$\zbbbar$ and $\zudsbar$, selected from \mbox{$\sim\!1\,400\, 000$}~$\zzero$ deca ys collected by \delphi in 1994. The results are compared to the predictions of the \jetset string fragmentation model and the \herwig cluster fragmentation model. The Modified Leading Logarithm Ap proximation with Local Parton-Hadron Duality is tested. The $\xipst$ dependence on the primary quark flavour is investigated and quantified for the different particle distributions. The $\pipm$, $ \kapm$, p and $\pbar$ multiplicities are measured with precisions from $\pm4$\%~to~$\pm6$\%. For the $\zqqbar$ and $\zbbbar$ event samples, these improve on previous measurements. The $\pipm$, $\k apm$, p and $\pbar$ multiplicities for $\zudsbar$ are presented for the first time.