title: Approximation of supremum and infimum processes as a stochastic approach to the providing of homeostasis
metadata.name: dc.contributor.author
metadata.value: Beliavsky, Grigory I.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Danilova, Natalia V.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Ougolnitsky, Gennady A.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2022-06-23T13:07:57Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2022-06-23T13:07:57Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2022-03
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Beliavsky G. I., Danilova N. V., Ougolnitsky G. A. Approximation of supremum and infimum processes as a stochastic approach to the providing of homeostasis. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 2022, vol. 18, iss. 1, pp. 5–17.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu10.2022.101
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/36928
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: We consider the calculation of bounded functional of the trajectories of a stationary diffusion
  process. Since an analytical solution to this problem does not exist, it is necessary to
  use numerical methods. One possible direction for obtaining the numerical method is applying
  the Monte Carlo (MC) method. This involves reproducing the trajectory of a random
  process with subsequent averaging over the trajectories. To simplify the reproduction of the
  trajectory, the Girsanov transform is used in this paper. The main goal is to approximate the
  supremum and infimum processes, which allows us to more accurately compute the mathematical
  expectation of a function depending on the values of the supremum and infimum
  processes at the end of the time interval compared to the classical method. The method
  is based on randomly dividing the interval of the time axis by stopping times passages of
  the Wiener process, approximating the density to replace the measure, and using the MC
  method to calculate the expectation. One of the applications of the method is the task of
  keeping a random process in a given area   the problem of homeostasis.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: This work was supported by Russian Science Foundation (project N 17-19-01038).
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. Applied Mathematics. Computer Science. Control Processes;Volume 18; Issue 1
metadata.lang: -
metadata.name: dc.subject
metadata.value: diffusion
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Monte-Carlo method
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Girsanov transform
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: homeostasis
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Approximation of supremum and infimum processes as a stochastic approach to the providing of homeostasis
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 5-17.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/36928/1/5-17.pdf
resources.format: Adobe PDF
resources.size: 406,16 kB