Publication result detail

Stochastic differential equations describing systems with coloured noise

KOLÁŘOVÁ, E.; BRANČÍK, L.

Original Title

Stochastic differential equations describing systems with coloured noise

English Title

Stochastic differential equations describing systems with coloured noise

Type

Scopus Article

Original Abstract

In this paper we deal with stochastic differential equations, that describe systems effected by coloured noise. In electrical systems this can be the case, when e.g. transmission line is modelled by means of proper higher-order ladder network. We define the mathematical representation of the coloured noise as a solution of the Langevin equation and formulate the corresponding It\^{o} type stochastic differential equation. Applying this theory we derive the stochastic model of the network and find sets of individual stochastic trajectories numerically via a stochastic version of the backward Euler scheme. Afterwards respective confidence intervals are computed statistically while utilizing Student's t distribution. The theoretical results are illustrated by an example of a higher-order ladder network. Numerical simulations in the example are carried out using Matlab.

English abstract

In this paper we deal with stochastic differential equations, that describe systems effected by coloured noise. In electrical systems this can be the case, when e.g. transmission line is modelled by means of proper higher-order ladder network. We define the mathematical representation of the coloured noise as a solution of the Langevin equation and formulate the corresponding It\^{o} type stochastic differential equation. Applying this theory we derive the stochastic model of the network and find sets of individual stochastic trajectories numerically via a stochastic version of the backward Euler scheme. Afterwards respective confidence intervals are computed statistically while utilizing Student's t distribution. The theoretical results are illustrated by an example of a higher-order ladder network. Numerical simulations in the example are carried out using Matlab.

Keywords

Stochastic integral equations; Wiener process; Ito formula; white noise; coloured noise; higher-order ladder network; transmission line model

Key words in English

Stochastic integral equations; Wiener process; Ito formula; white noise; coloured noise; higher-order ladder network; transmission line model

Authors

KOLÁŘOVÁ, E.; BRANČÍK, L.

RIV year

2019

Released

31.12.2018

Publisher

Mathematical Institute, Slovak Academy of Sciences

Location

Bratislava

ISBN

1210-3195

Periodical

Tatra Mountains Mathematical Publications

Volume

1

Number

71

State

Czech Republic

Pages from

99

Pages to

107

Pages count

9

URL

https://www.sav.sk/index.php?lang=en&doc=journal-list&part=article_response_page&journal_article_no=15631

BibTex

@article{BUT153204,
  author="Edita {Kolářová} and Lubomír {Brančík}",
  title="Stochastic differential equations describing systems with coloured noise",
  journal="Tatra Mountains Mathematical Publications",
  year="2018",
  volume="1",
  number="71",
  pages="99--107",
  doi="10.2478/tmmp-2018-0009",
  issn="1210-3195",
  url="https://www.sav.sk/index.php?lang=en&doc=journal-list&part=article_response_page&journal_article_no=15631"
}

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