title: On extremes of PSI-processes and gaussian limits of their normalized independent identical distributed sums
metadata.name: dc.contributor.author
metadata.value: Rusakov, Oleg V.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Ragozin, Roman A.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2022-07-07T21:39:30Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2022-07-07T21:39:30Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2022-06
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Rusakov O.V., Ragozin R.A. On extremes of PSI-processes and gaussian limits of their normalized independent identical distributed sums. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2022, vol. 9 (67), issue 2, pp. 269–277.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/spbu01.2022.208
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/37106
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: We define PSI-process — Poisson Stochastic Index process, as a continuous time random
  process which is obtained by a manner of a randomization for the discrete time of a random
  sequence. We consider the case when a double stochastic Poisson process generates this randomization,
  i. e. such Poisson process has a random intensity. Under condition of existence
  of the second moment the stationary PSI-processes possess a covariance which coincides
  with the Laplace transform of the random intensity. In our paper we derive distributions
  of extremes for a one PSI-process, and these extremes are expressed in terms of Laplace
  transform of the random intensity. The second task that we solve is a convergence of the
  maximum of Gaussian limit for normalized sums of i. i. d. stationary PSI-processes. We obtain
  necessary and sufficient conditions for the intensity under which, after proper centering
  and normalization, this Gaussian limit converges in distribution to the double Exponential
  Law. For solution this task we essentially base on the monograph: M.R.Leadbetter, Georg Lindgren, Holder Rootzen (1986) “Extremes and Relative Properties of Random Sequences
  and Processes”, end essentially use the Tauberian theorem in W. Feller form.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: This work is supported by Russian Foundation for Basic Research (grant no. 20-01-00646 А).
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Mathematics. Mechanics. Astronomy;Volume 9 (67); Issue 2
metadata.lang: -
metadata.name: dc.subject
metadata.value: pseudo-poissonian type processes
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: random intensity
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Laplace transform for distributions
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Tauberian theorems
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: On extremes of PSI-processes and gaussian limits of their normalized independent identical distributed sums
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 269-277.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/37106/1/269-277.pdf
resources.format: Adobe PDF
resources.size: 282,39 kB