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Feedback between stationary stochastic processes

IEEE Transactions on Automatic Control, 1975
A simple formulation is given for the notion of feedback between two stationary stochastic processes in terms of the canonical representation of the joint process. The definition presented here has an equivalent formulation in terms of filtering theory, and provides statistical criteria for the detection of feedback.
Caines, Peter E., Chan, C. W.
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Extension of Stationary Stochastic Processes

Theory of Probability & Its Applications, 1964
It is shown in this paper that if a continuous stationary stochastic process is given on the unit interval, a stationary extension of the given process exists on the whole line.
Parthasarathy, K. R., Varadhan, S. R. S.
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Simulation of stationary stochastic processes

Proceedings of the Institution of Electrical Engineers, 1968
A ‘spectral-factorisation’ procedure involving the solution of a Riccati matrix differential equation is considered to determine systems which, with white-noise input signals, may be used in the simulation of stochastic processes having prescribed stationary covariances. More spe$itically, the specification of a system is made so that the covariance of
J.B. Moore, B.D.O. Anderson
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Generation of non-Gaussian stationary stochastic processes

Physical Review E, 1996
A procedure is developed to generate a non-Gaussian stationary stochastic process with the knowledge of its first-order probability density and the spectral density. The procedure is applicable to an arbitrary probability density if the spectral density is of a low-pass type, and to a large class of probability densities if the spectral density is of a
, Cai, , Lin
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Stationary min-stable stochastic processes

Probability Theory and Related Fields, 1984
We consider the class of stationary stochastic processes whose margins are jointly min-stable. We show how the scalar elements can be generated by a single realization of a standard homogeneous Poisson process on the upper half-strip \([0,1]\times R_+\) and a group of \(L_ 1-isometries\).
de Haan, L. F. M., Pickands, James III
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