In the specific case of a single freight vehicle often returning to the LB of a mall, having a weakly stationary sequence of parking durations means that its recorded PDs at the observed mall vary randomly around the mean with a constant standard deviation, and the mean PD does not change over time.
Therefore, a temporally stationary sequence of DC components is reconstructed over time by a single coefficient.
Lemma 2.5 Let {X n, n ≥ 1} be a strictly stationary sequence of ρ--mixing random variables with EX n = 0 and ∑ n = 2 ∞ C o v X 1, X n < ∞, a n i, 1 ≤ i ≤ n, n ≥ 1 be an array of real numbers such that sup n ∑ i = 1 n a n i 2 < ∞ and max 1 ≤ i ≤ n a n i → 0 as n → ∞.
The reconstruction of a stationary sequence is based on its first coefficient.
The correlation of a stationary sequence must vanish after few samples.
A central limit theorem is obtained for stationary linear process of the form X t = ∑ j = 0 ∞ a j ε t - j, where {ε i } is strictly stationary sequence of linearly negative quadrant dependent random variables with Eε i = 0, E | ε i | s < ∞ for some s > 2, and ∑ j = 0 ∞ a j < ∞.
We focus on the extremal properties in the correlated and stationary sequence of characteristics of interest X 1,…,X n which is a function of the node sequence, the one actually generated by sampling algorithms.
We consider randomized algorithms to sample the nodes and study extremal properties in any associated stationary sequence of characteristics of interest like node degrees, number of followers, or income of the nodes in online social networks, which satisfy two mixing conditions.
For the stationary sequences of associated and negatively associated, Cai and Roussas [15] gave the notation μ ( n ) = ∑ j = n ∞ ∣ Cov ( X 1, X j + 1 ) ∣ 1 / 3 and supposed that μ(1) < ∞.
