On a Class of Non-Markovian Processes and Its Application to the Theory of Shot Noise and Barkhausen Noise

Abstract

Stochastic processes arising from overlapping pulses have been the center of interest for many years in many physical problems involving noise. A naive approach to such problems consists in assuming the statistical independence of pulses generated at different times and then studying the response function which is a sum of determinate functions of the random times at which the pulses have been generated. However, in the case of noise problems, there is ample experimental evidence to indicate the crude nature of the approximation. In fact, the pulses have a fairly good correlation, particularly those whose times of generation are not separated by very large intervals of time. To be precise, we may say that the stochastic process governing the distribution of the pulse numbers is essentially non-Markovian in character, and earlier studies relating to the study of the response function are based on the simple Markovian nature of a process. Recently, we have attempted to remove the restriction and explain a certain class of noise problems on the basis of a non-Markovian model governing the pulse generation (see Refs. 1–3). The present discussion will be confined to the particular model and we shall see how a number of physical phenomena and, in particular, shot noise and Barkhausen noise can be explained in terms of this model.