The existence of shift for periodically correlated processes and its boundedness are investigated. Spectral criteria for these non-stationary processes to have such shifts are obtained.

The paper considers empirical distribution functions of stationary causal processes. Weak convergence of normalized empirical distribution functions to Gaussian processes is established and sample path properties are discussed. The Chibisov-O’Reilly Theorem is generalized to dependent random variables. The proposed dependence structure is related to the sensitivity measure, a quantity appearing...

In this paper we discuss some recent advances in modeling and identiication of stationary processes. We point out that identiication of linear state-space models for stationary signals can be seen as stochastic realization of wide-sense stationary processes in an appropriate background Hilbert space. The geometric theory of stochastic realization developed in the last two decades plays an impor...

If A is a finite alphabet, U ⊂ Z, and μU is a probability measure on A that “looks like” the marginal projection of a stationary stochastic process on A D , then can we “extend” μU to such a process? Under what conditions can we make this extension ergodic, (quasi)periodic, or (weakly) mixing? After surveying classical work on this problem when D = 1, we provide some sufficient conditions and s...

Abstract In this paper, we will discuss the problem of chaos and control of a stochastic lattice gas model for prey-predator. Such system follows a stochastic dynamics composed of three Markovain sub-processes which are the birth of prey; the death of prey and simultaneous birth of predator, and spontaneous death of predator. The stability analysis and chaos of the stationary states of one-site...

In the paper a stochastic control model is studied, that admits a diffusion approximation. In the prelimit model the disturbances are given by noise processes of various types: additive stationary noise, rapidly oscillating processes, and discontinuous processes with large intensity for jumps of small size. We show that a feedback control, that satisfies a Lipschitz condition and is δ−optimal f...

Long-range correlated processes are ubiquitous, ranging from climate variables to financial time series. One paradigmatic example for such processes is fractional Brownian motion (fBm). In this work, we highlight the potentials and conceptual as well as practical limitations when applying the recently proposed recurrence network (RN) approach to fBm and related stochastic processes. In particul...

Vector sequences which are stationary with respect to polynomial hypergroups arise in various fields, such as stochastic processes and difference equations. In this paper, we discuss analytic properties of these sequences, namely the representation and complexification of the vector sequence.