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) |
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. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Shot_effect&oldid=48691
This article was adapted from an original article by A.N. Shiryaev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098.
See original article