Applications of second order stochastic integral equations to electrical networks

Abstract

The theory of stochastic differential equations is used in various fields of science and engineering. This paper deals with vector-valued stochastic integral equations. We show some applications of the presented theory to the problem of modelling RLC electrical circuits by noisy parameters. From practical point of view, the second-order RLC circuits are of major importance, as they are the building blocks of more complex physical systems. The mathematical models of such circuits lead to the second order differential equations. We construct stochastic models of the RLC circuit by replacing a coefficient in the deterministic system with a noisy one. In this paper we present the analytic solution of these equations using the Itô calculus and compute confidence intervals for the stochastic solutions. Numerical simulations in the examples are performed using Matlab.