A Kushner approach for small random perturbations of the Duffing-van der Pol system

The stochastic version of the Duffing-van der Pol system (SDvdP), which assumes the structure of a non-linear stochastic differential equation, is an appealing and a standard case from the stochastic systems' point of view, since it involves linear and non-linear vector fields, i.e. system non-linearities, state-independent and state-dependent stochastic accelerations. This paper discusses and explores the efficacy of three non-linear filters, which are developed using the Kushner equation, for the stochastic differential system of concern here. This paper introduces the notion of a qualitative analysis to decide a structure of the observation equation for non-linear stochastic filtering as well.