Characterization and identifiability for stochastic processes (Q2734975)

A wide scope of results on characterization and identifiability for different types of stochastic processes is reviewed. Many theorems contain characteristic properties of the Wiener process with linear mean function within the class of stochastically continuous processes with independent increments expressed by using the distributional properties of stochastic integrals with continuous nonrandom integrands, through the independence or conditional distributions of such integrals. Some criteria of this type are given for the Lévy stable, gamma or negative binomial processes. A broad group of results are related to the martingale and conditional structure characterization of the Wiener, Poisson, diffusion or Gaussian processes. Several characteristic properties for the Poisson type processes within the class of point processes are presented. Some interesting miscellaneous characterizations for stochastic processes are also discussed.NEWLINENEWLINEFor the entire collection see [Zbl 0961.60001].