If the first and second order moments of the process do not change with time then the process is
weak sense stationary
quasi stationary
strict sense stationary
non stationary
Weak sense stationary
The correct answer is: strict sense stationary.
A process is considered to be strict sense stationary if both the first moment (mean) and the second moment (variance) of the process remain constant over time. Specifically, this means that the mean and variance of the process do not change with the shifting of time.
If only the second order moment (variance) remains constant while the first order moment (mean) changes, then the process is called weak sense stationary.
If neither the first nor second order moments remain constant, the process is referred to as non-stationary.
Therefore, in the given scenario, if both the first and second order moments of the process do not change with time, the process can be classified as strict sense stationary.
To determine which option is the correct answer, we need to understand the concepts of weak sense (or wide-sense), strict sense (or narrow-sense) stationary, and non-stationary processes.
1. Weak sense stationary: A process is said to be weak sense stationary if its mean and autocovariance functions are time-invariant. In other words, the first and second order moments (mean and autocovariance) remain constant over time.
2. Strict sense stationary: A process is said to be strict sense stationary if its probability distribution remains unchanged when shifted by any fixed time period. This means that the joint probability distribution of any finite set of time points is the same, regardless of the starting time.
3. Non-stationary: A process is considered non-stationary if it does not satisfy the conditions of either weak sense or strict sense stationarity. This means that either the mean or the autocovariance (or both) change with time.
Based on the given information, if the first and second order moments of the process do not change with time, then the correct answer would be "weak sense stationary." This is because weak sense stationarity requires that the mean and autocovariance remain constant over time, which aligns with the given condition. The other options, quasi-stationary and non-stationary, are not applicable in this case.