Stochastic processes associated with random divisions of a line

Abstract

A class of stochastic processes associated with points randomly distributed in a line of finite extension L, is considered. A general integral equation for the function representing the probability distribution of the stochastic variable under consideration is derived and solved by using the Laplace transform technique. Examples of the above class of processes are cited. In particular, the problem of the fluctuations in brightness of the Milky Way is discussed in detail. The results of Chandrasekhar and Munch in regard to this astrophysical problem are derived in a simple and direct manner.