Telegraph process

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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]

Properties

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:

Application

This random process finds wide application in model building:

See also

References

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