Shot effect

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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


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



[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:
This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098