B.I. Yakubovich – Ph.D.(Phys.-Math.), Senior Research Scientist, 
Petersburg Nuclear Physics Institute named by B.P. Konstantinov of NRC «Kurchatov Institute»
E-mail: yakubovich_bi@pnpi.nrcki.ru

Fluctuation processes are studied theoretically and their spectra are calculated in essentially important cases. The purpose is to obtain expressions that can be used to describe the spectra of large number of fluctuation processes of different physical nature. The relevance of research is connected to the following circumstances. Fluctuational phenomena are very various by nature. There are numerous mechanisms for the appearance of fluctuations. Fluctuation phenomena are widely studied. Researches on a number of the directions in this area have fundamental value. Study of fluctuations also has an applied value. Noises are usually considered as a harmful factor. Noises limit the parameters of electronic devices. This, first of all, affects for work of receiving and measuring devices. In this regard studying of noises is necessary for finding of ways of decrease in their level. Besides, perhaps useful application of noise. Measurements of noise apply to non-destructive quality control and assessment of reliability of products of electronic technique.
At present, extensive studies of fluctuation phenomena are being carried out, both fundamental and applied. Such researches are carried out in numerous objects and cover various branches of physics. When analyzing fluctuations, their characteristics are calculated. Important and largely determining characteristic of fluctuation process is its spectrum. The calculation of spectra is carried out for specific processes and, accordingly, under given conditions. It seems expedient to calculate the expressions for spectra of fluctuation processes in rather general form in order to use them for solving numerous problems on the study of fluctuations.
Fluctuational processes have various physical nature. At the same time very large number of fluctuational processes can be presented as a random sequence of pulses. Fluctuation processes of this type are analyzed and their spectra are calculated. In essence important cases are considered. First, the spectrum of fluctuation process is calculated in rather general form. Fluctuational process in the following case is analyzed: duration and amplitude of a pulse statistically are connected, pulse amplitude statistically is connected to amplitude of previous pulse, statistical connections are set in general form. As a result expression for spectrum of fluctuational process in rather general case is calculated. There are statistical connections between parameters of a pulse and between parameters of serial pulses, distribution functions of parameters are set in general form. Spectra of fluctuation processes in other principal cases are considered. Expression is obtained for the spectrum of fluctuation process, when there are statistical connections between the parameters of pulse and distribution functions of the parameters of pulse are given in general form. Expression for the spectrum of fluctuation process is obtained, when the parameters of pulses are statistically independent, distribution functions of pulses parameters are given in general form.
The results of this article are as follows. Fluctuations that can be represented as a random sequence of pulses are investigated. Fluctuation processes are studied for different types of statistical connections between the parameters of process. The spectrum of fluctuation process is calculated in rather general case: there are statistical connections between the parameters of pulse and between the parameters of serial pulses, distribution functions of the parameters are given in general form. Expressions are obtained for the spectra of fluctuation processes in a number of in essence important cases. The calculated expressions are applicable for describing the spectra of large number of fluctuation processes of different physical nature. The results of the article can be used to analyze numerous fluctuation phenomena. The obtained results can be widely applied in carrying out both fundamental and applied studies of fluctuation phenomena.

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