The dynamics of high-inertia particles in the logarithmic layer of a wall turbulent flow has been studied using Lagrangian stochastic simulation. Because of the linear dependence of the turbulent time scale on the distance to the wall in the logarithmic layer, turbophoresis, i.e., the migration of particles toward the wall, is observed. It has a nonlocal character in the wall region because of a significant contribution of ballistic motion of particles. The profiles of the concentration and second moment of particle velocities have been obtained for an arbitrary inertia parameter of a particle and different values of the restitution coefficient of the particle velocity at rebound from the wall. It has been shown that the probability density distribution of particle velocities has “heavy tails” in the wall region. These tails exhibit a power-law behavior in the inelastic collapse regime for particle trajectories, which is observed at restitution coefficients below a critical value of 0.163 in agreement with the results reported in Belan et al., Phys. Rev. E 93, 052206 (2016).