<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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 Itô 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 confi-dence 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.</p></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 Itô 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 confi-dence 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.

Stochastic Differential Equations Describing Systems with Coloured Noise

Tatra Mountains Mathematical Publications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Stochastic Differential Equations Describing Systems with Coloured Noise"}

In this paper we deal with stochastic differential equations, that describe systems effected by coloured noise. In electrical systems this can be the case,...

Stochastic Differential Equations Describing Systems with Coloured Noise

Published Online: Jan 25, 2019

Page range: 99 - 107

Received: Dec 11, 2017

DOI: https://doi.org/10.2478/tmmp-2018-0009

Keywords
Stochastic integral equations, Wiener process, Itô formula, white noise, coloured noise, higher-order ladder network, transmission line model

© 2018 Edita Kolářová et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Stochastic Differential Equations Describing Systems with Coloured Noise

Published Online: Jan 25, 2019

Page range: 99 - 107

Received: Dec 11, 2017

DOI: https://doi.org/10.2478/tmmp-2018-0009

KeywordsStochastic integral equations, Wiener process, Itô formula, white noise, coloured noise, higher-order ladder network, transmission line model

© 2018 Edita Kolářová et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Stochastic integral equations, Wiener process, Itô formula, white noise, coloured noise, higher-order ladder network, transmission line model