The VIMOS Public Extragalactic Redshift Survey (VIPERS): The growth of
  structures at $0.5<z<1.2$ from redshift-space distortions in the clustering
  of the PDR-2 final sample
  We present measurements of the growth rate of cosmological structure from the
modelling of the anisotropic galaxy clustering measured in the final data
release of the VIPERS survey. The analysis is carried out in configuration
space and based on measurements of the first two even multipole moments of the
anisotropic galaxy auto-correlation function, in two redshift bins spanning the
range $0.5 < z < 1.2$. We provide robust and cosmology-independent corrections
for the VIPERS angular selection function, allowing recovery of the underlying
clustering amplitude at the percent level down to the Mpc scale. We discuss
several improvements on the non-linear modelling of redshift-space distortions
(RSD) and perform detailed tests of a variety of approaches against a set of
realistic VIPERS-like mock realisations. This includes using novel fitting
functions to describe the velocity divergence and density power spectra
$P_{\theta\theta}$ and $P_{\delta\theta}$ that appear in RSD models. These
tests show that we are able to measure the growth rate with negligible bias
down to separations of $5h^{-1}Mpc$. Interestingly, the application to real
data shows a weaker sensitivity to the details of non-linear RSD corrections
compared to mock results. We obtain consistent values for the growth rate times
the matter power spectrum normalisation parameter of $f\sigma_8=0.55\pm 0.12$
and $0.40\pm0.11$ at effective redshifts of $z = 0.6$ and $z=0.86$
respectively. These results are in agreement with standard cosmology
predictions assuming Einstein gravity in a $\Lambda \rm{CDM}$ background.
