Continuous-discrete models refer to systems describedby continuous ordinary or stochastic differential equations,with measurements acquired at discrete sampling instants.Here we investigate the state estimation problem for suchsystems in the stochastic framework, for a class of nonlinearsystems characterized by a linear drift and a generic nonlineardiffusion term. Motivation stems from a large variety ofapplications, ranging from systems biology to finance. By usinga Carleman linearization approach we show how the originalsystem can be embedded into an infinite dimensional bilinearsystem, for which it is possible to write the equations of theoptimal linear filter, in case of measurements provided by linearstate transformations. A finite dimensional approximation of theoptimal linear filter is finally derived. Results are applied to acase of interest in financial applications.

Optimal linear filter for a class of nonlinear stochastic differential systems with discrete measurements

CACACE F;PAPI M
2017-01-01

Abstract

Continuous-discrete models refer to systems describedby continuous ordinary or stochastic differential equations,with measurements acquired at discrete sampling instants.Here we investigate the state estimation problem for suchsystems in the stochastic framework, for a class of nonlinearsystems characterized by a linear drift and a generic nonlineardiffusion term. Motivation stems from a large variety ofapplications, ranging from systems biology to finance. By usinga Carleman linearization approach we show how the originalsystem can be embedded into an infinite dimensional bilinearsystem, for which it is possible to write the equations of theoptimal linear filter, in case of measurements provided by linearstate transformations. A finite dimensional approximation of theoptimal linear filter is finally derived. Results are applied to acase of interest in financial applications.
2017
978-150902873-3
Filtering of stochastic systems; Carleman linearization; Continuous-discrete systems
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.12610/16153
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