A stochastic perspective of RL electrical circuit using different noise terms

Abstract

PurposeThe purpose of this paper is to analyze the effect of the white, colored and mixture noise perturbations as Gaussian process on the parameters of the RL electrical circuit including potential source and resistance.Design/methodology/approachBy adding different noise terms in the voltage and resistance parameters of an RL electrical circuit, the deterministic model is replaced by a stochastic differential equation (SDE).FindingsOwing to the application of multiple Ito's formula the analytical solutions of resulted SDEs have been obtained. Furthermore, based on a numerical method involving Euler‐Maruyama scheme, the solution of the problem at the point of interest as a continuous time stochastic process has been obtained. Also shown is that the confidence interval for mean of solutions with colored and mixture noises is better than white noise.Practical implicationsNumerical tests via Matlab programming are performed in order to show the efficiency and accuracy of the present work. Numerical experiments show that an excellent estimation on the solution can be obtained within a couple of minutes time at Pentium IV‐2.4 GHz PC.Originality/valueIt is believed that the stochastic model of an RL circuit with colored and mixture noises in potential source has not been studied before. Furthermore, according to latest information from the research works, two stochastic parameters in voltage and resistance of RL circuit including colored and mixture noise processes have been investigated for the first time in this paper.