Confidence intervals for RLCG cell influenced by coloured noise

The purpose of the paper is to determine confidence intervals for the stochastic solutions in RLCG cells with coloured noise influenced potential source. 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 Ito stochastic calculus. Equations for the first and the second moment of the stochastic solution of the coloured noise effected RLCG cell are obtained and the corresponding confidence intervals are determined. The moment equations lead to ordinary differential equations, which are solved numerically by the implicit Euler scheme, which turns out to be very effective. For comparison the confidence intervals are computed also statistically by an implementation of the Euler scheme to stochastic differential equations. The theoretical results are illustrated by examples. Numerical simulations in the examples are carried out using Matlab.