On the stochastic process of random noise

Abstract

If events are arrivals of electrons at the anode of vacuum tube, (l l) represents the noise current. The formulation (1.1) is due to J. L. Doob ί 1 ) Formally, the extensive analysis of random noise was done by S. O Rice, in the case \ t Ct) is a trigonometric polynomial. The object of this paper is to prove some results, in connection with Rice theory, with X, (t) defined by (1.1) in a rather rigorous way from mathematical view points. The proofs of some known results are contained, because of completeness