The idea of the collisionless relaxation of the stellar disk of the Milky Way is elaborated. Jeans' gravitationally unstable stellar disk is considered by applying the procedure of the quasi-linear kinetic approach. It is shown that unstable gravity perturbations (e.g., those produced by a spontaneous disturbance) grow almost aperiodically in the main part of the disk between the inner and outer Lindblad resonances and affect the in-plane averaged velocity distribution of stars. The diffusion equation in velocity space is derived describing the secular increase in the dispersion of the peculiar velocities of stars with time after star formation in the rotationally supported Galactic disk. Our previous investigation is extended by including the minor second-order terms of the theory to describe the small distortion in the local distribution function of stars away from the standard Schwarzschild distribution. It is shown that the residual velocity distributions along the radial and azimuthal coordinates in velocity space are non-Gaussian in the sense that the central peaks are more populated and the higher energy portions of the distributions are somewhat underpopulated. For a subsystem of relatively old stars with ages (2-3)×109 years, the quantitative change is of the order of 10%-15%. The observational test of the theory is also suggested.
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