title: Time distribution from zero up to beginning of the final stop of semi-Markov diffusion process on interval with unattainable boundaries
metadata.name: dc.contributor.author
metadata.value: Harlamov, Boris P.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Rasova, Sofia S.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2022-10-20T16:42:11Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2022-10-20T16:42:11Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2022-09
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Harlamov B. P., Rasova S. S. Time distribution from zero up to beginning of the final stop of semi-Markov diffusion process on interval with unattainable boundaries. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2022, vol. 9 (67), issue 3, pp. 517–526. https://doi.org/10.21638/spbu01.2022.312 (In Russian)
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/spbu01.2022.312
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/38309
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: A one-dimensional process with continuous trajectories on non-negative semi-axis is considered.
  The process has the Markov property with respect to the first exit time from any
  open interval (semi-Markov process). This process is called to be diffusion if probability for its first exit point from any symmetric neighborhood of its initial point across any boundary
  tends to 1/2 as length of this neighborhood tends to zero. Time distribution from zero up
  to beginning of the final interval of constancy is investigated. This distribution depends
  on semi-Markov transition generating functions of the process. Representation for Laplace
  transform of this distribution is obtained in an integral form. The integrand of this representation
  explains sense of quadratic members of Tailor decomposition of a semi-Markov
  transition generating function by powers of diameter of symmetric neighborhood of the process
  initial point. Namely trajectory of the process has no any final interval of constancy if
  and only if coefficient of such a quadratic member is equal to zero.
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 3
metadata.lang: -
metadata.name: dc.subject
metadata.value: continuous semi-Markov process
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: semi-Markov chain
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: final interval of constancy
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: differential equation
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Laplace transformation
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: unattainable boundary
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: integral representation
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Time distribution from zero up to beginning of the final stop of semi-Markov diffusion process on interval with unattainable boundaries
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 517-526.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/38309/1/517-526.pdf
resources.format: Adobe PDF
resources.size: 293,27 kB