Please use this identifier to cite or link to this item: https://hdl.handle.net/2440/17856
Citations
Scopus Web of Science® Altmetric
?
?
Type: Journal article
Title: General smoothing formulas for Markov-modulated Poisson observations
Author: Elliott, R.
Malcolm, W.
Citation: IEEE Transactions on Automatic Control, 2005; 50(8):1123-1134
Publisher: IEEE-Inst Electrical Electronics Engineers Inc
Issue Date: 2005
ISSN: 0018-9286
Statement of
Responsibility: 
Elliott, R.J. Malcolm, W.P.
Abstract: In this paper, we compute general smoothing dynamics for partially observed dynamical systems generating Poisson observations. We consider two model classes, each Markov modulated Poisson processes, whose stochastic intensities depend upon the state of an unobserved Markov process. In one model class, the hidden state process is a continuously-valued ItÔ process, which gives rise to a continuous sample-path stochastic intensity. In the other model class, the hidden state process is a continuous-time Markov chain, giving rise to a pure jump stochastic intensity. To compute filtered estimates of state process, we establish dynamics, whose solutions are unnormalized marginal probabilities; however, these dynamics include Lebesgue–Stieltjes stochastic integrals. By adapting the transformation techniques introduced by J. M. C. Clark, we compute filter dynamics which do not include these stochastic integrals. To construct smoothers, we exploit a duality between our forward and backward transformed dynamics and thereby completely avoid the technical complexities of backward evolving stochastic integral equations. The general smoother dynamics we present can readily be applied to specific smoothing algorithms, referred to in the literature as: Fixed point smoothing, fixed lag smoothing and fixed interval smoothing. It is shown that there is a clear motivation to compute smoothers via transformation techniques similar to those presented by J. M. C. Clark, that is, our smoothers are easily obtained without recourse to two sided stochastic integration. A computer simulation is included.
Description: © Copyright 2005 IEEE
DOI: 10.1109/TAC.2005.852565
Appears in Collections:Applied Mathematics publications
Aurora harvest 6

Files in This Item:
There are no files associated with this item.


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.