Document Type : Research Paper

Authors

• R. Rezaeyan ¹
• R. Farnoush ¹
• E. B. Jamkhaneh ²

¹ Department of Mathematics, Faculty of Basic Sciences, Islamic Azad University, Sciences and Research Branch, Tehran, Iran.

² Department of Mathematics, Islamic Azad University Ghaemshahr Branch, Ghaemshahr, Iran.

Abstract

In this paper, we present an application of the stochastic calculus to the problem of modeling electrical networks. The filtering problem have an important role in the theory of stochastic differential equations(SDEs). In this article, we present an application of the continuous Kalman-Bucy filter for an RL circuit. The deterministic model of the circuit is replaced by a stochastic model by adding a noise term in the source. The analytic solution of the resulting stochastic integral equations are found using the Ito formula.

Keywords

• Stochastic differential equation
• white noise
• Kalman-Bucy filter
• Ito formula
• analytic solution