On bounds for the variance of the number of zeros of a differentiable Gaussian stationary process

Autor: R. N. Miroshin
Rok vydání: 2015
Předmět:
Zdroj: Vestnik St. Petersburg University: Mathematics. 48:82-88
ISSN: 1934-7855
1063-4541
Popis: It is known that the variance of the number of zeros of a differentiable Gaussian stationary process whose correlation function has spectrum with a continuous component can be represented by the integral of a complicated function. Previously, the author obtained both upper and lower bounds for this integral in analytical form under certain conditions. In this paper, these conditions are checked for several classes of processes, which include first-order Markov processes and two classes of analytic processes. It is also shown that the variance of the number of zeros can be obtained by means of these bounds for a process the correlation function of which has a spectrum with no continuous component. For a certain analytic process, the variance of the number of zeros can be expressed in terms of ele-mentary functions (such formulas have previously been known for only two processes).
Databáze: OpenAIRE
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