Purpose
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.
Design/methodology/approach
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.
Practical implications
Numerical examples are performed using MATLAB programming to show the efficiency and accuracy of the present work.
Originality/value
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.
This paper presents a new explicit method, called the truncated Milstein method for the numerical solution of some stochastic differential equations. This new method was fixed under the local Lipschitz condition as well as the khasminskii-type condition. Our numerical experiments based on the obtained method demonstrate the applicability and effectiveness of the results in the evaluation of a wide range of linear and nonlinear financial problems. This new method has high convergence in comparison with the Euler, Milstein and truncated Euler methods for some linear and nonlinear stochastic differential equations.
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