Fading Random Evolution on a Complex Plane

The article explores a generalization of the Goldstein-Kac model, specifically a model of random evolution on a complex plane, with the velocity that decreases over time. This process simulates the motion of a particle in a force field, among other phenomena. Limit theorems describing the distribution of the absorbing point for this process have been derived. Additionally, nonlinear integral equations for functionals of the process have been obtained, and the existence and uniqueness of their solutions have been proven.