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Confidence intervals for RLCG cell influenced by coloured noise

Edita Kolarova (Department of Mathematics, Brno University of Technology, Brno, Czech Republic)
Lubomir Brancik (Department of Radio Electronics, Brno University of Technology, Brno, Czech Republic)



The purpose of this paper is to determine confidence intervals for the stochastic solutions in RLCG cells with a potential source influenced by coloured noise.


The deterministic model of the basic RLCG cell leads to an ordinary differential equation. In this paper, a stochastic model is formulated and the corresponding stochastic differential equation is analysed using the Itô stochastic calculus.


Equations for the first and the second moment of the stochastic solution of the coloured noise-affected RLCG cell are obtained, and the corresponding confidence intervals are determined. The moment equations lead to ordinary differential equations, which are solved numerically by an implicit Euler scheme, which turns out to be very effective. For comparison, the confidence intervals are computed statistically by an implementation of the Euler scheme using stochastic differential equations.

Practical implications/implications

The theoretical results are illustrated by examples. Numerical simulations in the examples are carried out using Matlab. A possible generalization for transmission line models is indicated.


The Itô-type stochastic differential equation describing the coloured noise RLCG cell is formulated, and equations for the respective moments are derived. Owing to this original approach, the confidence intervals can be found more effectively by solving a system of ordinary differential equations rather than by using statistical methods.



This work was supported by Czech Science Foundation under grant number 15-18288S. For research, the infrastructure of the SIX Centre was used.


Kolarova, E. and Brancik, L. (2017), "Confidence intervals for RLCG cell influenced by coloured noise", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 36 No. 4, pp. 838-849.



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