Limit theorems for some polynomial statistics of the Poisson process (Q1897264)

The central limit theorem and a theorem on large deviations are established for the distribution of a \(U\)-statistic of an inhomogeneous Poisson process \(X(t)\), \(0 \leq t \leq T\), as \(T \to \infty\). The proofs make use of formulas for the cumulants for this statistic and a general lemma of large deviations due to Saulis and Statulevičius.