Fast Filtering in Switching Approximations of Non-linear Markov Systems with Applications to Stochastic Volatility

Abstract : We consider the problem of optimal statistical filtering in general non-linear non-Gaussian Markov dynamic systems. The novelty of the proposed approach consists in approximating the non-linear system by a recent Markov switching process, in which one can perform exact and optimal filtering with a linear time complexity. All we need to assume is that the system is stationary (or asymptotically stationary), and that one can sample its realizations. We evaluate our method using two stochastic volatility models and results show its efficiency.
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Ivan Gorynin, Stéphane Derrode, Emmanuel Monfrini, Wojciech Pieczynski. Fast Filtering in Switching Approximations of Non-linear Markov Systems with Applications to Stochastic Volatility. IEEE Transactions on Automatic Control, Institute of Electrical and Electronics Engineers, 2017, 62 (2), pp.853-862. ⟨10.1109/TAC.2016.2569417⟩. ⟨hal-01448538⟩

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