In this work the risk-sensitive optimal filtering equations for systems of third grade with linear observations and mean square cost criterion to be minimized had been applied to the Fitz Hugh-Nagumo model. This special model represents a excitable system. The performance of the obtained risk-sensitive estimator for third degree stochastic systems with polynomial linear drift terms with polynomial observations equations is verified, comparing the mean-square criteria values in final time for the optimal risk-sensitive estimator and polynomial filtering equations. The goal of this work is to experiment applying both filtering equations: risk-sensitive and polynomial to third degree polynomial systems, comparing the results obtained in this special model. It is observed that when the value of D is greater than 1, the risk-sensitive equations present a singularity. However, the estimates are better than the polynomial filtering equations with respect to the values of the proposed mean square cost criterion to be minimized.

No abstract

No abstract

No abstract

No abstract