On a non-linear stochastic dynamic circuit using Stratonovich differential

The stochastic differential equation is the standard approach to analyse dynamic circuits in noisy environments. Ignoring non-linearity as well as inaccurate stochastic interpretations will have influence on the state estimation procedure and control of dynamic circuits. This paper intends to develop the mathematical theory of a non-linear time-varying stochastic system, a noisy sampling mixer, an appealing non-linear stochastic dynamic circuit of digital communication systems. In this paper, we formalin the sampling mixer that assumes the structure of a non-linear time-varying Stratonovich SDE (Stochastic Differential Equation) in lieu of a bilinear time-varying It (o) over cap SDE. Subsequently, the theory of the noise-influenced sampling mixer is achieved using the following influential results of stochastic processes: (i) the It (o) over cap -Stratonovich integral relationship and (ii) stochastic differential rules. After utilising these two results of stochastic processes, we derive the conditional moment evolutions of the sampling mixer. Importantly, the noise analysis of this paper confirms the consensus on the It (o) over cap -Stratonovich calculi dilemma as well as accounts for square non-linearity. This paper is useful for applied mathematicians as well as stochastic dynamists looking for applications of Stratonovich stochastic methods to potential practical problems, which are relatively very scarce in the literature. (C) 2014 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.