  The term active nematics designates systems in which apolar elongated
particles spend energy to move randomly along their axis and interact by
inelastic collisions in the presence of noise. Starting from a simple
Vicsek-style model for active nematics, we derive a mesoscopic theory, complete
with effective multiplicative noise terms, using a combination of kinetic
theory and It\^o calculus approaches. The stochastic partial differential
equations thus obtained are shown to recover the key terms argued in EPL
\textbf{62} (2003) 196 to be at the origin of anomalous number fluctuations and
long-range correlations. Their deterministic part is studied analytically, and
is shown to give rise to the long-wavelength instability at onset of nematic
order (see arXiv:1011.5408). The corresponding nonlinear density-segregated
band solution is given in a closed form.
