Kargovsky AV, Chichigina OA. Integrated random pulse process with positive and negative periodicity.
Phys Rev E 2022;
106:024103. [PMID:
36109971 DOI:
10.1103/physreve.106.024103]
[Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/21/2022] [Accepted: 07/14/2022] [Indexed: 06/15/2023]
Abstract
A study of nonstationary processes that are integrals of stationary random sequences of delta pulses is presented. An integrated renewal process can be represented as the sum of a deterministic linear function of time and a Wiener process of the corresponding intensity. This intensity is determined by the mean value and variance of the waiting times of the pulse process and is greater for super-Poisson processes than for sub-Poisson ones. Linear growth over time of all cumulants is proved. An integrated random process with fixed time intervals can be replaced by the sum of a deterministic linear function and a random process with bounded variance. The analytical results are in good agreement with the numerical ones.
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