In many application areas, Lévy processes, a generalization of the Wiener process, are widely used in order to suitably capture sudden shifts or discrete-value nature in stochastic dynamical systems. In this paper, we formulate a weighting function conversion problem for weak approximation of Lévy processes. This problem covers many practically important problems, and is shown to be equivalent to a sampled-data H2 signal reconstruction problem. By virtue of a remarkable feature of Lévy processes, the main result provides a simple design procedure of suboptimal filters for this problem.
This paper considers system identification for linearly approximated models. Linear approximation models are useful for identification, but their accuracy may not be estimated by the conventional linear identification methods. This paper proposes a method to evaluate not only the system parameters but also the influence of the linear approximation errors in identification. The method is based on particle filters, which are known for its applicability to a wide class of nonlinear systems. Numerical examples are given to demonstrate the effectiveness of the proposed method in detail. Furthermore, experimental validation is performed for a simple pendulum system.