Risk-sensitive filtering and smoothing for continuous-time Markov Processes

Author

Malcolm, W. Paul ; Elliott, Robert J. ; James, Matthew R.

Author_Institution

Nat. ICT Australia (NICTA), Canberra, ACT, Australia

Volume

51

Issue

5

fYear

2005

fDate

5/1/2005 12:00:00 AM

Firstpage

1731

Lastpage

1738

Abstract

We consider risk sensitive filtering and smoothing for a dynamical system whose output is a vector process in R². The components of the observation process are a Markov process observed through a Brownian motion and a Markov process observed through a Poisson process. Risk-sensitive filters for the robust estimation of an indirectly observed Markov state processes are given. These filters are stochastic partial differential equations for which robust discretizations are obtained. Computer simulations are given which demonstrate the benefits of risk sensitive filtering.

Keywords

Brownian motion; Markov processes; continuous time filters; filtering theory; partial differential equations; stochastic processes; Brownian motion; Poisson process; continuous-time Markov processes; risk-sensitive filtering-smoothing; stochastic partial differential equations; Australia Council; Filtering; Filters; Information technology; Markov processes; Robustness; Signal processing; Smoothing methods; State-space methods; Stochastic processes; Change of measure; martingales; risk-sensitive filtering;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/TIT.2005.846405

Filename

1424311