Mathematical analysis of random noise.

*(English)*Zbl 0063.06487Introduction: In this section we use the representations of the noise currents given in section 2.8 to derive some statistical properties of \(I(t)\). The first six sections are concerned with the probability distribution of \(I(t)\) and of its zeros and maxima. Sections 3.7 and 3.8 are concerned with the statistical properties of the envelope of \(I(t)\). Fluctuations of integrals involving \(I^2(t)\) are discussed in section 3.9. The probability distribution of a sine wave plus a noise current is given in 3.10 and in 3.11 an alternative method of deriving the results of Part III is mentioned. Prof. Uhlenbeck has pointed out that much of the material in this Part is closely connected with the theory of Markov processes. Also S. Chandrasekhar has written a review of a class of physical problems which is related, in a general way, to the present subject [Rev. Mod. Phys. 15, 1–89 (1943; Zbl 0061.46403)].