title: To the history of Saint-Petersburg school of Probability and Statistics. III. Functional distributions, stochastic geometry and extrema
metadata.name: dc.contributor.author
metadata.value: Borodin, Andrey N.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Davydov, Yuriy A.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Nevzorov, Valeriy B.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2018-12-13T14:25:44Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2018-12-13T14:25:44Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2018-12
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Borodin A.N., Davydov Yu.A., Nevzorov V. B. To the history of Saint- Petersburg school of Probability and Statistics. III. Functional distributions, stochastic geometry and extrema. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2018, vol. 5 (63), issue 4, pp. 572–596.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: 10.21638/11701/spbu01.2018.404
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/15126
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: This is the third article in a series of surveys dedicated to the scientific achievements of
  the Leningrad —Saint-Petersburg school of Probability and Statistics in the period from
  1947 to 2017. It is devoted to some studies of functionals of random processes, some problems
  of stochastic geometry and some questions connected with ordered systems of random
  variables. In the first section of the article, we talk about problems of calculation of distributions
  for various functionals of Brownian motion. The so-called invariance principles are
  also considered for Brownian local times and random walks. The second section is devoted
  to limit theorems for weakly dependent random variables and to local limit theorems for
  stochastic functionals. A method of stratifications and the local invariance principle are
  also mentioned. In the following section, we consider the asymptotic behavior of convex
  hulls of random samples and limit theorems for random zonotopes. An important relation
  between Poisson point processes and stable distributions is discussed. In the final part, we
  provide exhaustive information on research related to ordered systems of random variables.
  The maxima of consecutive sums, order statistics and record values are considered in detail.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: Работа выполнена при частичной финансовой поддержке СПбГУ-ННИО (грант №6.65.37.2017) и РФФИ (грант №18-01-00393).
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 5 (63); Issue 4
metadata.lang: -
metadata.name: dc.subject
metadata.value: Brownian motion
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: distribution of functionals
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Brownian local time
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: random walk
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: invariance principle
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: fibering method
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: local invariance principle
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: limit theorems
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: random zonotopes
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: convex hulls
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: order statistics
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: extrema
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: records
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: To the history of Saint-Petersburg school of Probability and Statistics. III. Functional distributions, stochastic geometry and extrema
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 04-Borodin.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/15126/1/04-Borodin.pdf
resources.format: Adobe PDF
resources.size: 402,07 kB