In gravitational lensing, the microlensing effect is explained by the fact that the stars from the lens galaxy are modifying the light that reaches us from the distant source, and so generating microimages. In order to study it, we take into account the effect of the stars transferred to the plane of the object, whose geometric representation is called a caustic.

In particular, we can use the counting of caustic crossing events to estimate the peculiar velocity of lens galaxies. We simulate the motion of the stars in the lens galaxy instead of considering an effective contribution of the stellar velocity field. To do that, we infer the PDF of the peculiar velocity using dynamical microlensing magnification maps. This way, we are trying to obtain a good estimation of peculiar velocities to acquire a better understanding of the cosmological parameters.