2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/224820We consider the problem of hypotheses testing with the basic simple hypothesis: observed sequence of points corresponds to stationary Poisson process with known intensity. The alternatives are stationary self-exciting point processes. We consider one-sided parametric and one-sided nonparametric composite alternatives and construct locally asymptotically uniformly most powerful tests. The results of numerical simulations of the tests are presented.23 pages, 6 figuresStatistics Theorytext