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The purpose of this paper is to analyze the effects of white noise perturbations of the input voltage on the band pass filter response, both on pass band and reject band.

By adding white noise term in the input voltage of the filter circuit, the deterministic ordinary differential equation (ODE) is replaced by a stochastic differential equation (SDE). With the application of Ito lemma, the analytical solution of SDE has been obtained. Furthermore, based on the Euler–Maruyama approximation, the numerical simulation for SDE has been done.

Numerical examples are performed using MATLAB programming to show the efficiency and accuracy of the present work.

All previous noise analyses of filter circuits were done using ODEs or component noise formulas in the electrical domain. The stochastic perspective for these circuits is adopted for the first time in this paper.

The 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.

By 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).

Owing 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.

Numerical 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.

It 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.