The same is stationarity, which generally refers to width stationarity, mathematical expectation is constant, and EXtXs is only related to time difference.
In mathematics, stationary random process or strictly stationary SSS process (SSS) is a random process, and its probability distribution at a fixed time and position is the same as that at all times and positions. In this way, the parameters of mathematical expectation and variance do not change with time and position.
For example, white noise (AWGN) is a stationary process, while the percussion of cymbals is non-stationary. Although the percussion sound of cymbals is basically white noise, this noise changes with time: it is quiet before percussion and gradually weakens after percussion.
Independent incremental process, stationary independent incremental process with discrete state is a special Markov process. Poisson process and Brownian motion are its special cases. After the sum of the parts of the essentially independent random variable sequence is separated from the general independent incremental process, the remaining parts are always random and continuous.