Transactions of the Institute of Systems, Control and Information Engineers
Online ISSN : 2185-811X
Print ISSN : 1342-5668
ISSN-L : 1342-5668
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Sampled-Data H2 Signal Reconstruction Approach to Weak Approximation Problem for Lévy Processes
Kenji Kashima
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2011 Volume 24 Issue 10 Pages 241-249

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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.

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© 2011 The Institute of Systems, Control and Information Engineers
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