The applicaton of the author´s kinetic equations for non-Markovian processes for some non-linear statistical analysis problems are considered. Two types of no trivial non-linear effects are investigated. The first is the non-linear dynamic system driven by the Markovian binary process. The second is the systems having some restricted area of the functioning. This area is determined by some deterministic bounds. The main advantage of this method is the reduction of the problem dimension in all statistical analysis problems with the comparison of the Markovian approach.