Vector Stochastic Differential Equations Used to Electrical Networks with Random Parameters

In this paper we present an application of the It stochastic calculus to the problem of modelling RLC electrical circuits. The deterministic model of the circuit is replaced by a stochastic model by adding a noise term to various parameters of the circuit. The analytic solutions of the resulting stochastic integral equations are found using the multidimensional It formula. For the numerical simulations in the examples we used MATLABr. The SDE approach has its perspectives in the simulation even higher-order circuits representing more complex physical systems, as their real implementations are often subject to a number of random effects. An example for a transmission line lumped-parameter model is provided.