Multiplicative Kalman filtering
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We study a non-linear Hidden Markov Model, where the process of interest is the absolute value of a discretely observed Ornstein–Uhlenbeck diffusion, which is observed after a multiplicative perturbation. We obtain explicit formulae for the recursive relations which link the relevant conditional distributions. As a consequence the predicted, filtered, and smoothed distributions for the hidden process can easily be computed. We illustrate the behaviour of these distributions on simulations.
KeywordsFiltering Discrete time observations Hidden Markov Models Parametric inference Scale perturbation
Mathematics Subject Classification (2000)60G35 62M05 60J60
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- Di Masi GB, Runggaldier WJ, Barozzi B (1983) Generalized finite-dimensional filters in discrete time. In: Nonlinear stochastic problems (Algarve, 1982), NATO adv sci inst ser C math phys sci, vol 104. Reidel, Dordrecht, pp 267–277. Google Scholar