Stochastic differential equations describing systems with coloured noise
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26220%2F18%3APU130468" target="_blank" >RIV/00216305:26220/18:PU130468 - isvavai.cz</a>
Result on the web
<a href="https://www.sav.sk/index.php?lang=en&doc=journal-list&part=article_response_page&journal_article_no=15631" target="_blank" >https://www.sav.sk/index.php?lang=en&doc=journal-list&part=article_response_page&journal_article_no=15631</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.2478/tmmp-2018-0009" target="_blank" >10.2478/tmmp-2018-0009</a>
Alternative languages
Result language
angličtina
Original language name
Stochastic differential equations describing systems with coloured noise
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>SC</sub> - Article in a specialist periodical, which is included in the SCOPUS database
CEP classification
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OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
<a href="/en/project/GA15-18288S" target="_blank" >GA15-18288S: Research of signal integrity at high-speed interconnects</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Tatra Mountains Mathematical Publications
ISSN
1210-3195
e-ISSN
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Volume of the periodical
1
Issue of the periodical within the volume
71
Country of publishing house
CZ - CZECH REPUBLIC
Number of pages
9
Pages from-to
99-107
UT code for WoS article
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EID of the result in the Scopus database
2-s2.0-85061429474