The sequence of difference indicator matrices {Δ t′} is stationary Markov and ergodic.
Finally, the stationarity of the channel, see Section 2.3, implies that the sequence of difference matrices {Δ t′} is stationary.
In the following, we will show that the number of distinct difference indicator matrices is finite for bounded N, and that the sequence of difference indicator matrices {Δ t′} is stationary Markov and ergodic.
We are now in a position to introduce the main technical result of this section, which shows that the sequence of augmented state variables {Ξ t } in (17) and the sequence of difference indicator matrices {Δ t′} in (20) are jointly Markovian and form a Markov jump linear system.
Pairwise comparisons of concatenated amino acid sequences revealed sequence differences of 5.8% (OTU-C versus OTU-G), 18% (OTU-C versus OTU-J) and 10.0% (OTU-G versus OTU-J) (Table 4).
Since statistical results are not easily comprehensible, whereas sequences of difference images again need sequential viewing [4, 14].
Let be a sequence of martingale differences, and let be a sequence of positive real numbers with.
When the distance is computed for a series of adjacent video frames, the result will be a sequence of frame differences, FD-sequence for short.
In addition, Wang and Yang [13] established a strong limit theorem for arbitrary stochastic sequences in 2005, which generalized Chow's [5] series convergence theorem for sequence of martingale differences.
Next one needs the sequence of forward differences among 1, 2, 3, 4,...; this is just 1, 1, 1, 1,..
