Howtosignalprocessing
A random process is called stationary to order, one or first order stationary if its 1st order density function does not change with a shift in time origin. In other words, f X (x 1 , t 1 ) = f X (x 1 , t 1 + C)must be true for any t1 and any real number C if X(t1) is to be a first order stationary process.
- What is stationary random process?
- What is first order stationary?
- What is second-order random process?
What is stationary random process?
A random process at a given time is a random variable and, in general, the characteristics of this random variable depend on the time at which the random process is sampled. A random process X(t) is said to be stationary or strict-sense stationary if the pdf of any set of samples does not vary with time.
What is first order stationary?
First-order stationarity - These series have a mean constant over time. Any other statistics (like variance) can change at the different points in time. Second-order stationarity (also called weak stationarity) - These time series have a constant mean and variance over time.
What is second-order random process?
A second-order random process Xt:t∈T is one for which E[X2t] is finite (indeed bounded) for all t∈T.
