title: Pseudo-poissonian processes with stochastic intensity and a class of processes which generalize the Ornstein Uhlenbeck process
metadata.name: dc.contributor.author
metadata.value: Rusakov, Oleg V.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2017-07-19T09:58:34Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2017-07-19T09:58:34Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2017-06
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Rusakov O.V. Pseudo-poissonian processes with stochastic intensity and a class of processes which generalize the Ornstein Uhlenbeck process. Vestnik SPbSU. Mathematics. Mechanics. Astronomy, 2017, vol. 4 (62), issue 2, pp. 247–257.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: 10.21638/11701/spbu01.2017.208
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/6947
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: The definition of pseudo-poissonian processes is given in the famous monograph of William Feller, vol. II,
  chapter X. The modern development of the theory of information flows stipulates a new interest to detailed
  analysis of behavior and characteristics of the pseudo-poissonian processes. Formally, pseudo-poissonian
  process is a poissonian subordination of the mathematical time of an independent random sequence,
  the time randomization of a random sequence. We consider the given sequence as independent identically
  distributed random values with second moments. Although in this case the pseudo-poissonian processes do
  not have independent increments it is possible to calculate the autocovariance function with the property of
  the exponentially decreasing. Normalized sums of independent copies of such Pseudo-Poissonian processes
  tend to the Ornstein Uhlenbeck process. We consider a generalization of the driving poissonian process
  to the case of a random intensity. We show that under this generalization the autocovariance function of
  the corresponding Pseudo-Poissonian process is the Laplace transform of the distribution of this random
  intensity. We shortly discuss stochastic principles to choice of the distribution of the random intensity and
  illustrate them in two detailed examples. Refs 20. Figs 2.
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 4 (62); Issue 2
metadata.lang: -
metadata.name: dc.subject
metadata.value: pseudo-poissonian 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: Ornstein—Uhlenbeck type processes
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Pseudo-poissonian processes with stochastic intensity and a class of processes which generalize the Ornstein Uhlenbeck process
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 08-Rusakov.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/6947/1/08-Rusakov.pdf
resources.format: Adobe PDF
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