The question of completeness of the spectral domain generated by a bimeasure is discussed. The bimeasure is derived from a spectral representation of a given process of weak class (C). In particular by an example it is shown that the spectral domain of a weak class (C) process is not necessarily...

We construct a.s. nonlinear regression representations of general stochastic processes . As a consequence we obtain in particular special regression representations of Markov chains and of certain m-dependent sequences. For m-dependent sequences we obtain a constructive method to check, whether...

We consider optimal stopping of independent sequences. Assuming that the corresponding imbedded planar point processes converge to a Poisson process we introduce some additional conditions which allow to approximate the optimal stopping problem of the discrete time sequence by the optimal...

For a class of point processes including nonhomogeneous Poisson processes, some Cox processes and some processes of non-Poisson type, the question of existence and construction of complete and sufficient statistics is investigated. The results are based on the generalization of some results from...