Howtosignalprocessing
- What does it mean to say that a stochastic process is stationary?
- What is autocorrelation in stochastic process?
- What are the 3 Conditions for a stochastic process to be weakly stationary?
- What is jointly wide-sense stationary process?
What does it mean to say that a stochastic process is stationary?
In mathematics and statistics, a stationary process (or a strict/strictly stationary process or strong/strongly stationary process) is a stochastic process whose unconditional joint probability distribution does not change when shifted in time.
What is autocorrelation in stochastic process?
The autocorrelation function provides a measure of similarity between two observations of the random process X(t) at different points in time t and s. The autocorrelation function of X(t) and X(s) is denoted by RXX(t, s) and defined as follows: (10.2a) (10.2b)
What are the 3 Conditions for a stochastic process to be weakly stationary?
A stochastic process Xt is weakly stationary if it meets these three conditions: The mean of the process is constant. That is, E(Xt)=μ E ( X t ) = μ (where μ is some constant) for all values of t . The second moment of Xt , or E(X2t) E ( X t 2 ) , is finite.
What is jointly wide-sense stationary process?
Jointly stationary (or wide-sense stationary) processes are a collection of random processes that satisfy the same property as stationary (or WSS) processes, even when considering also joint distributions of variables from more than one sequence in the collection.
