The displacement probability and diffusion time in q-space magnetic resonance measurements that use finite-duration diffusion-encoding gradients are discussed. Two basic physical ways of treating the diffusion phenomenon in probability terms for the finite-δ case are described. The form of the average of the displacement-specific dephasing in case of homogeneous non-restricted Gaussian diffusion are obtained by statistical analysis. Simulations are made to study the range of applicability of this formalism for the case of non-homogeneous non-restricted diffusion, and restricted diffusion inside a spherical domain.