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 Itô calculus approaches. The stochastic partial differential equations thus obtained are shown to recover the key terms argued in Ramaswamy et al (2003 Europhys. Lett. 62 196) 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 Shi X and Ma Y 2010 arXiv:1011.5408). The corresponding nonlinear density-segregated band solution is given in a closed form.