Optimal prediction of compound mixed Poisson processes

The paper examines best linear unbiased prediction of compound mixed Poisson processes where typical stipulations such as conditional or unconditional independence of the increments are weakened.Explicit representations of the optimal forecast, its asymptotic distribution and the minimum mean square error are established. The article also discusses applications to special processes of risk theory including Pólya–Lundberg processes and nonstationary Poisson processes with time-dependent arrival rates.