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Linear filtering of systems with memory

Preprint Series # 657
Inoue, Akihiko and Nakano, Yumiharu and Anh, Vo Linear filtering of systems with memory. (2004);

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Abstract

We study the linear filtering problem for systems driven by continuous Gaussian processes with memory described by two parameters. The driving processes have the virtue that they possess stationary increments and simple semimartingale representations simultaneously. It allows for straightforward parameter estimations. After giving the semimartingale representations of the processes by innovation theory, we derive Kalman-Bucy-type filtering equations for the systems. We apply the result to the optimal portfolio problem for an investor with partial observations. We illustrate the tractability of the filtering algorithm by numerical implementations.

Item Type:Preprint
Uncontrolled Keywords:Filtering, systems with memory, stationary increment processes, innovation processes, Gaussian processes, portfolio optimization
Subjects:60-xx PROBABILITY THEORY AND STOCHASTIC PROCESSES
ID Code:340

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  • Linear filtering of systems with memory. (deposited 27 Jul 2004) [Currently Displayed]