Filtering for Discrete-Time Markov Processes and Applications to Inventory Control with Incomplete Information

THE OXFORD HANDBOOK OF NONLINEAR FILTERING, D. Crisan and B. Rozovsky, eds., Chapter 18, pp. 500-525, Oxford University Press, 2011

20 Pages Posted: 30 Jan 2008 Last revised: 25 Apr 2012

See all articles by Alain Bensoussan

Alain Bensoussan

University of Texas at Dallas - Naveen Jindal School of Management

M. Çakanyıldırım

University of Texas at Dallas - Naveen Jindal School of Management

Suresh Sethi

University of Texas at Dallas - Naveen Jindal School of Management

Abstract

We develop a general filtering framework for the problem of estimating the state of a system whose dynamics is governed by a discrete-time Markov process. We describe applications to inventory control systems with partial observations. We introduce conditional distributions and unnormalized conditional probabilities to transform nonlinear transition equations into linear ones. Moreover, this transformation greatly facilitates our study of the stochastic optimal control problems governed by nonlinear transition equations.

Keywords: Filtering, inventory control, optimal control, adaptive control, unnormalized probability, Kalman filter, Zakai equation, partial observations, incomplete information

JEL Classification: C61, M11, D81, D83

Suggested Citation

Bensoussan, Alain and Cakanyildirim, Metin and Sethi, Suresh, Filtering for Discrete-Time Markov Processes and Applications to Inventory Control with Incomplete Information. THE OXFORD HANDBOOK OF NONLINEAR FILTERING, D. Crisan and B. Rozovsky, eds., Chapter 18, pp. 500-525, Oxford University Press, 2011 , Available at SSRN: https://ssrn.com/abstract=1087656 or http://dx.doi.org/10.2139/ssrn.1087656

Alain Bensoussan

University of Texas at Dallas - Naveen Jindal School of Management ( email )

800 West Campbell Rd
SM 30
Richardson, TX 75080-3021
United States
9728836117 (Phone)

HOME PAGE: http://www.utdallas.edu/~axb046100/

Metin Cakanyildirim

University of Texas at Dallas - Naveen Jindal School of Management ( email )

P.O. Box 830688
Richardson, TX 75083-0688
United States

Suresh Sethi (Contact Author)

University of Texas at Dallas - Naveen Jindal School of Management ( email )

800 W. Campbell Road, SM30
Richardson, TX 75080-3021
United States

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