The implementation of linearized operators describing inter- and like-species collisions in the global gyrokinetic particle-in-cell code ORB5 [ S. Jolliet, Comput. Phys. Commun. 177, 409 (2007) ] is presented. A neoclassical axisymmetric equilibrium with self-consistent electric field can be obtained with no assumption made on the radial width of the particle trajectories. The formulation thus makes it possible to study collisional transport in regions where the neoclassical approximation breaks down such as near the magnetic axis. The numerical model is validated against both analytical results as well as other simulation codes. The effects of the poloidally asymmetric Fourier modes of the electric field are discussed, and the contribution of collisional kinetic electrons is studied. In view of subsequent gyrokinetic simulations of turbulence started from a neoclassical equilibrium, the problem of numerical noise inherent to the particle-in-cell approach is addressed. A novel algorithm for collisional gyrokinetic simulation switching between a local and a canonical Maxwellian background for, respectively, carrying out the collisional and collisionless dynamics is proposed, and its beneficial effects together with a coarse graining procedure [ Y. Chen and S. E. Parker, Phys. Plasmas 14, 082301 (2007) ] on noise and weight spreading reduction are discussed.