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
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
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