# Confidence intervals for RLCG cell influenced by coloured noise

Confidence intervals for RLCG cell influenced by coloured noise PurposeThe purpose of this paper is to determine confidence intervals for the stochastic solutions in RLCG cells with a potential source influenced by coloured noise.Design/methodology/approachThe 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.FindingsEquations 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/implicationsThe 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.Originality/valueThe 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering Emerald Publishing

# Confidence intervals for RLCG cell influenced by coloured noise

, Volume 36 (4): 12 – Jul 3, 2017
12 pages

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# References (25)

Publisher
Emerald Publishing
ISSN
0332-1649
DOI
10.1108/COMPEL-07-2016-0321
Publisher site
See Article on Publisher Site

### Abstract

PurposeThe purpose of this paper is to determine confidence intervals for the stochastic solutions in RLCG cells with a potential source influenced by coloured noise.Design/methodology/approachThe 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.FindingsEquations 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/implicationsThe 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.Originality/valueThe 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.

### Journal

COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic EngineeringEmerald Publishing

Published: Jul 3, 2017