Sampled-Data H² Signal Reconstruction Approach to Weak Approximation Problem for Lévy Processes

Abstract

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.