Detail publikace

Stochastic differential equations describing systems with coloured noise

KOLÁŘOVÁ, E. BRANČÍK, L.

Originální název

Stochastic differential equations describing systems with coloured noise

Typ

článek v časopise ve Scopus, Jsc

Jazyk

angličtina

Originální abstrakt

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.

Klíčová slova

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

Autoři

KOLÁŘOVÁ, E.; BRANČÍK, L.

Vydáno

31. 12. 2018

Nakladatel

Mathematical Institute, Slovak Academy of Sciences

Místo

Bratislava

ISSN

1210-3195

Periodikum

Tatra Mountains Mathematical Publications

Ročník

1

Číslo

71

Stát

Česká republika

Strany od

99

Strany do

107

Strany počet

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"
}