Large deviation principles for the processes admitting embedded compound renewal processes
For a stochastic process \(X(t)\) with trajectories space of functions without discontinuities of the second kind and right continuous and admitting embedded compound renewal processes (CRP), this paper establishes first the large deviation principle (LDP) for the normalized process \(x_T=X(T)/T\) and then a trajectory moderate deviation principle in the Cramér case as well as in the so-called semiexponential case is derived. These results are used to study large deviations for the trajectories of a periodic CRP with delay and a semi-Markov CRP.
scientific article; zbMATH DE number 7466390
scientific article