Stochastic approach for noise analysis and parameter estimation for RC and RLC electrical circuits

‎The main focus of this paper is to examine the effects of Gaussian white noise and Gaussian colored noise perturbations on the voltage of RC and RLC electrical circuits‎. ‎For this purpose‎, ‎the input voltage is assumed to be corrupted by the white noise and the charge is observed at discrete time points‎. ‎The deterministic models will be transferred to stochastic differential equations and these models will be solved analytically using Ito's lemma‎. ‎Random colored noise excitations‎, ‎more close to real environmental excitations‎, ‎so Gaussian colored noise is considered in these electrical circuits‎. ‎Scince there is not always a closed form analytical solution for stochastic differential equations‎, ‎then these models will be solved numerically based on the Euler‎- ‎maruyama scheme‎. ‎The parameter estimation for these stochastic models is investigated using the least square estimator when the parameters are missing data that it is a concern in electrical engeineering‎. ‎Finally‎, ‎some numerical simulations via Matlab programming are carried out in order to show the efficiency and accuracy of the present work‎.