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Stochastic differential equations describing systems with coloured noise

In: Tatra Mountains Mathematical Publications, vol. 71, no. 1
Edita Kolářová - Lubomír Brančík
Detaily:
Rok, strany: 2019, 99 - 107
Jazyk: eng
Kľúčové slová:
Stochastic integral equations, Wiener process, It\^{o} formula, white noise, coloured noise, higher-order ladder network, transmission line model
Typ článku: Mathematics
Typ dokumentu: Mathematics
O článku:
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.
Ako citovať:
ISO 690:
Kolářová, E., Brančík, L. 2019. Stochastic differential equations describing systems with coloured noise. In Tatra Mountains Mathematical Publications, vol. 71, no.1, pp. 99-107. 1210-3195. DOI: https://doi.org/10.2478/tmmp-2018-0009

APA:
Kolářová, E., Brančík, L. (2019). Stochastic differential equations describing systems with coloured noise. Tatra Mountains Mathematical Publications, 71(1), 99-107. 1210-3195. DOI: https://doi.org/10.2478/tmmp-2018-0009
O vydaní:
Vydavateľ: MÚ SAV
Publikované: 2. 1. 2019