In probability theory, the telegraph process is a memoryless continuous-time stochastic process that shows two distinct values. It models burst noise (also called popcorn noise or random telegraph signal). If the two possible values that a random variable can take are and , then the process can be described by the following master equations:

and

. The process is also known under the names Kac process (after mathematician Mark Kac), and dichotomous random process.

Solution

,

where

is the transition rate matrix) by

1. .

It can be shown that

given by

Properties

Knowledge of an initial state decays exponentially, 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:

• In physics, spin systems and fluorescence intermittency show dichotomous properties. But especially in single molecule experiments probability distributions featuring algebraic tails are used instead of the exponential distribution implied in all formulas above.

• In finance for describing share prices

• In biology for describing transcription factor binding and unbinding.

See also

• Markov chain

• List of stochastic processes topics

• Random telegraph signal

References