A novel approach to the theory of shot noise

The theory of shot effect is examined on the basis of an inhomogeneous Poisson process. The «Poisson» parameter A(t) characterising the stochastic process is generalized in such a manner that X itself becomes a random variable depending on the number and the position of events on the time axis. It is found that the number density of arrivals of electrons in the theory of shot effect has exactly the same behaviour as the process under consideration. Such a process is strongly non-Markovian. and the calculation of moments and correlation functions of the output turns out to be difficult. However it is shown that a knowledge of the moments of and the correlation of events on the t-axis is sufficient to determine these functions. The conjecture of Eowland regarding the behaviour of the mean square of the cumulative response for shot effect is proved and in addition an explicit expression for the power spectrum of the response is derived. Other physical phenomena which can be explained on the basis of the stochastic model are cited. © 1965 Società Italiana di Fisica.