ANALYTICAL RELATIONS FOR TIME-DEPENDENT STATISTICAL MICROLENSING

Gravitational field of randomly distributed point masses produces a stochastic angular shift Psi of the positions of a remote object image. We obtain characteristic functions and probability distributions of apparent proper motions u = d Psi/dt and angular accelerations a = d(2) Psi/dt(2) under the assumptions that the gravitator velocities are constant, the gravitator volume density is uniform in the directions orthogonal to the line of sight, and the microlensing process is linear. The nonuniformity corrections to the characteristic functions due to spatial variations of the gravitator density are estimated. These corrections appear to be essential for the u-distribution in the presence of bulk motions of gravitators; for the a-distribution they may be neglected.