Point processes with finite-dimensional conditional probabilities
A class of point processes on the real line is studied called rational arrival processes (RAP). This class is strictly larger than Neuts' (1979) Markovian arrival processes (MAP). While RAP allows for more general features like finite-dimensional distributions of interarrival times (which are matrix-exponential rather than phase type), their probabilistic interpretation is less clear: it is given in terms of a piecewise determininistic Markov process. Further properties like moments, Laplace transforms, Palm distributions, etc. are investigated.
scientific article; zbMATH DE number 1792514
scientific article