stationary stochastic process

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Noun1.stationary stochastic process - a stochastic process in which the distribution of the random variables is the same for any value of the variable parameter
stochastic process - a statistical process involving a number of random variables depending on a variable parameter (which is usually time)
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Typically, the active unit is attached to the stationary process equipment, such as a formulation vessel or filling line, and the passive unit is attached to the mobile container, such as a flexible bag or rigid intermediate bulk container (IBC).
Since the QBD X is formulated as time invariant, it is a stationary process. The infinitesimal generator matrix Q of the QBD process X is then given by
In a stationary process, the criterion for LMS algorithm to converge in the mean if 0 < u , and in the mean-square if 0 < u or R must be approximated.
[xi] = ([[xi].sub.1], [[xi].sub.2]) is a zero-mean widely stationary process, and E[[xi].sup.2.sub.1] = E[[xi].sup.2.sub.2] = 0.05; thus, K = 0.05.
In 1965, Priestley proposed evolutionary stochastic process [5] theory in which a nonstationary process is converted to an integral of a stationary process and a deterministic modulation function, and then, the time-varying spectrum density of the nonstationary process is obtained from the spectrum density of the stationary process, and a method of describing the characteristics of the spectrum of a nonstationary process and a model of nonstationary ground motion is created.
In the latter case, the time-series is said to be generated by a stationary process. If the parameter value is higher than the critical value for statistical significance, the analysis suggests that the time series has a trend.
Jitter is not a stationary process, and it can vary widely depending on the time at which it is observed.
In time series study, under some regular conditions on the stationary process, the periodogram is asymptotically unbiased estimator of spectral density; that is, [I.sub.n] ([omega]) [right arrow] f([omega]) as sample size n [right arrow] [infinity], where the bias is of order O([n.sup.-1]).
Limit theory for the sample acf of stationary process with heavy tails with applications to ARCH.
Since the drift and diffusion coefficients are time homogeneous, [a.sub.[alpha]](Y, t) = [a.sub.[alpha]](Y) and [B.sub.[alpha][beta]](Y, t) = [B.sub.[alpha][beta]](Y), (5) is a statistically stationary process and the solution of (6) converges to a stationary distribution, [12,Sec.
They introduced the corresponding statistics [U.sup.(n).sub.t] calculated according to the formulation of the Bollinger bands, which is a stationary process, and then they gave the law of large numbers since [{[U.sup.(n).sub.t+kn]}.sub.k=1,2,...]are mutually independent for each fixed t [greater than or equal to] 0.Thus the Bollinger bands property which seems unthinkable at first glance was proved.
For example, self-similar processes are obtained by applying the Lamperti operator on the time scale of a stationary process [4].