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Estimation and control for linear, partially observable systems with non-gaussian initial distribution

Author

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  • Benes, Václav E.
  • Karatzas, Ioannis

Abstract

The nonlinear filtering problem of estimating the state of a linear stochastic system from noisy observations is solved for a broad class of probability distributions of the initial state. It is shown that the conditional density of the present state, given the past observations, is a mixture of Gaussian distributions, and is parametrically determined by two sets of sufficient statistics which satisfy stochastic DEs; this result leads to a generalization of the Kalman-Bucy filter to a structure with a conditional mean vector, and additional sufficient statistics that obey nonlinear equations, and determine a generalized (random) Kalman gain. The theory is used to solve explicitly a control problem with quadratic running and terminal costs, and bounded controls.

Suggested Citation

  • Benes, Václav E. & Karatzas, Ioannis, 1983. "Estimation and control for linear, partially observable systems with non-gaussian initial distribution," Stochastic Processes and their Applications, Elsevier, vol. 14(3), pages 233-248, March.
    • Handle: RePEc:eee:spapps:v:14:y:1983:i:3:p:233-248
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    Cited by:

    1. Sebastian Jaimungal & Xiaofei Shi, 2024. "The Price of Information," Papers 2402.11864, arXiv.org, revised Mar 2024.
    2. Brennan, Michael J & Xia, Yihong, 2001. "Assessing Asset Pricing Anomalies," Review of Financial Studies, Society for Financial Studies, vol. 14(4), pages 905-942.
    3. Brendle, Simon, 2006. "Portfolio selection under incomplete information," Stochastic Processes and their Applications, Elsevier, vol. 116(5), pages 701-723, May.

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