Filtering for Fast Mean-Reverting Processes

Asymptotic Analysis, Vol. 70, Nos. 3-4, 2010, pp. 155-176

28 Pages Posted: 20 Oct 2012 Last revised: 2 Dec 2013

See all articles by Andrew Papanicolaou

Andrew Papanicolaou

NYU Tandon School of Engineering, Department of Finance and Risk Engineering

Date Written: April 15, 2010

Abstract

We consider nonlinear filtering applications to target tracking based on a vector of multi-scaled models where some of the processes are rapidly mean reverting to their local equilibria. We focus attention on target tracking problems because multiple scaled models with fast mean-reversion (FMR) are a simple way to model latency in the response of tracking systems. The main results of this paper show that nonlinear filtering algorithms for multi-scale models with FMR states can be simpli ed signi cantly by exploiting the FMR structures, which leads to a simplified Baum-Welch recursion that is of reduced dimension. We implement the simplified algorithms with numerical simulations and discuss their eciency and robustness.

Keywords: hidden Markov model, multiscale, filtering

Suggested Citation

Papanicolaou, Andrew, Filtering for Fast Mean-Reverting Processes (April 15, 2010). Asymptotic Analysis, Vol. 70, Nos. 3-4, 2010, pp. 155-176. Available at SSRN: https://ssrn.com/abstract=2164533

Andrew Papanicolaou (Contact Author)

NYU Tandon School of Engineering, Department of Finance and Risk Engineering ( email )

6 Metrotech Center
Brooklyn, NY 11201
United States

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