Abstract
This paper treats the filtering and parameter identification for the stochastic hyperbolic systems with jump noise processes. The physical situation of this model can be found in finance problem, e.g., the term structure of the bonds is a typical example. It is well-known that the filtering algorithm including jump processes is not possible to be a closed form like Kalman filter. We eliminate the jump process from the system dynamics by using one observation data and convert the system to the Gaussian frame work. After deriving the Kalman filter and the related likelihood function, the adaptive estimation algorithm is constructed with the aid of parallel filtering scheme. Some numerical examples are demonstrated.
