In probability theory, the telegraph process is a memoryless continuous-time stochastic process that shows two distinct values.
If these are called a and b, the process can be described by the following master equations:
and
The process is also known under the names Kac process[1] , dichotomous random process.[2]
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Knowledge of an initial state decays exponentially. Therefore for a time in the remote future, the process will reach the following stationary values, denoted by subscript s:
Mean:
Variance:
One can also calculate a correlation function:
This random process finds wide application in model building: