The theory of the mean square variation of a function formed by adding known functions with random phases, and applications to the theories of the shot effect and of light

Abstract

In the study of random events and associated fluctuations such as occur in the shot effect, a theorem first stated and discussed by Dr N. R. Campbell can often be employed. It applies on any occasion when there occur at random a number of events whose effects are additive. Let us suppose that a single event occurring at time tr causes at time t an effect f(t − tr) in some part of the observed system, and that the effects of different events are additive, so that the total effect or output is ϑ(t), given byWe may suppose that the same events cause another set of effects g(t − tr) with output ϑ(t), whereBoth the functions are assumed to be bounded and integrable in the Riemann sense, as are all the functions studied in physics.