# Shot effect

A mathematical description of voltage fluctuations at the output of a linear system at the input of which there are random perturbations produced at random moments of time. If is the output of the system at time resulting from a single pulse applied at time , the shot effect may be described by a stochastic process

where are the arrival moments of pulses, while are random variables characterizing the magnitudes of the intensities of the pulses. In the particular case when , , , the are independent, uniformly-distributed random variables with finite variance, while forms a Poisson flow of events with parameter , the process is a stationary stochastic process in the narrow sense, with

#### References

[1] | J.H. Laning, R.G. Battin, "Random processes in automatic control" , McGraw-Hill (1956) |

#### Comments

#### References

[a1a] | S.O. Rice, "Mathematical analysis of random noise" Bell Systems Techn. J. , 23 (1944) pp. 283–332 |

[a1b] | S.O. Rice, "Mathematical analysis of random noise" Bell Systems Techn. J. , 24 (1945) pp. 46–156 |

[a2] | N. Wax (ed.) , Selected papers on noise and stochastic processes , Dover, reprint (1953) |

[a3] | E. Parzen, "Stochastic processes" , Holden-Day (1962) |

[a4] | E. Wong, "Stochastic processes in information and dynamical systems" , McGraw-Hill (1971) |

**How to Cite This Entry:**

Shot effect. A.N. Shiryaev (originator),

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Shot_effect&oldid=15483