title: On some local asymptotic properties of sequences with a random index
metadata.name: dc.contributor.author
metadata.value: Rusakov, Oleg V.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Yakubovich, Yuriy V.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Baev, Budimir A.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2020-09-10T14:02:23Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2020-09-10T14:02:23Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2020-09
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Rusakov O. V., Yakubovich Yu. V., Baev B. A. On some local asymptotic properties of sequences with a random index. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2020, vol. 7 (65), issue 3, pp. 453–468.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/spbu01.2020.308
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/19396
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: We consider sequences of random variables with the index subordinated by a doubly
  stochastic Poisson process. A Poisson stochastic index process, or PSI-process for short,
  is a random process ψ(t) with the continuous time t which one can obtain via subordination of a sequence of random variables (ξj ), j = 0, 1, . . ., by a doubly stochastic Poisson
  process Π1(tλ) as follows: ψ(t) = ξΠ1(tλ)
  , t > 0. We suppose that the intensity λ is a nonnegative random variable independent of the standard Poisson process Π1. In the present
  paper we consider the case of independent identically distributed random variables (ξj )
  with a finite variance. R. Wolpert and M. Taqqu (2005) introduce and investigate a type of
  the fractional Ornstein — Uhlenbeck (fOU) process. We provide a representation for such
  fOU process with the Hurst exponent H ∈ (0, 1/2) as a limit of scaled and normalized
  sums of independent identically distributed PSI-processes with an explicitly given intensity λ. This fOU process, locally at t = 0, approximates in the square mean the fractional
  Brownian motion with the same Hurst exponent H ∈ (0, 1/2). We examine in details two
  examples with the intensity corresponding to the R. Wolpert and M. Taqqu’s fOU process:
  a telegraph process, arising for ξ0 having the Rademacher distribution ±1 with probabilities 1/2, and a PSI-process with the uniform distribution for ξ0. For these two examples we
  derive exact and asymptotic formulae for a local modulus of continuity over a small time
  interval for a single PSI-process.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: The work of O. V. Rusakov and Yu. V. Yakubovich was prepared with partial financial support of the Russian Foundation for Basic Research, project 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 7 (65); Issue 3
metadata.lang: -
metadata.name: dc.subject
metadata.value: fractional Ornstein — Uhlenbeck process
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: fractional Brownian motion
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: pseudoPoisson process
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: random intensity
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: telegraph process
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: modulus of continuity
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: On some local asymptotic properties of sequences with a random index
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 453-468.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/19396/1/453-468.pdf
resources.format: Adobe PDF
resources.size: 371,67 kB