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Stochastic Filtering for Diffusion Processes With Level Crossings

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3 Author(s)
Agostino Capponi ; Department of Industrial Engineering, Purdue University, West Lafayette, United States of America ; Ibrahim Fatkullin ; Ling Shi

We provide a general framework for computing the state density of a noisy system given the sequence of hitting times of predefined thresholds. Our method relies on eigenfunction expansion corresponding to the Fokker-Planck operator of the diffusion process. For illustration, we present a particular example in which the state and the noise are one-dimensional Gaussian processes and observations are generated when the magnitude of the observed signal is a multiple of some threshold value. We present numerical simulations confirming the convergence and the accuracy of the recovered density estimator. Applications of the filtering methodology will be illustrated.

Published in:

IEEE Transactions on Automatic Control  (Volume:56 ,  Issue: 9 )