A random process
is an uncountable
(in the case of a time-continuous random process) or countable
(in the case of a discrete
random process) collection
of random variable
s. Any given realization
of a random process is called a sample path
or sample function
of the random process.
Examples of random processes are found anywhere: electrocardiograms, sound signals, buffer contents, ftp throughput, random binary sequences, etc. are all random processes. Useful models of random processes include the random walk, the Poisson process and the Gaussian random process, which includes the Wiener process as a special case.
Random processes are primarily characterized by the joint cummulative distribution function and probability distribution function of a finite subset of their random variables. If the joint CDF of the process does not change at all with time, then the random process is called stationary. If this rather severe condition is not met, but the mean of the process is a constant and its autocovariance or autocorrelation is only a function of the delay, then the random process is called wide-sense stationary (WSS).
Tools for working with random processes include the autocovariance, autocorrelation, cross-correlation and correlation coefficient.