Large deviations in the theory of nonlinear filtering and nilpotent Lie algebras
type: Item
instance of: scholarly article
title: Large deviations in the theory of nonlinear filtering and nilpotent Lie algebras
zbMATH Open document ID: 0805.60018
published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques
publication date: 1995-02-02T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/77486
review text: Let \((X^ \varepsilon, Y^ \varepsilon)\) denote the signal-observation couple solving the Stratonovich SDE \[ \begin{aligned} dX^ \varepsilon_ t &= \varepsilon \sum_ j \widetilde{A}_ j (X^ \varepsilon_ t)\circ d\widetilde{B}_ t^{\varepsilon,j}+ A_ 0 (X^ \varepsilon_ t)dt+ \sum_ k A_ k (X^ \varepsilon_ t)\circ dY_ t^{\varepsilon,k},\\ dY_ t^ \varepsilon &= \Gamma(X^ \varepsilon_ t)dt+ dB_ t; \qquad X^ \varepsilon_ 0= x^ \varepsilon; \qquad Y^ \varepsilon_ 0=0.\end{aligned} \] If the Lie algebra generated by the vector fields \(A_ k\) is nilpotent, the conditional probabilities of the signal process \(X^ \varepsilon_ t\) (given the observation \(Y^ \varepsilon_ t\)) obey a large deviation principle. This result is applied to the theory of nonlinear filtering extending an earlier result by Doss.
Mathematics Subject Classification ID: 60F10
Mathematics Subject Classification ID: 60G35
zbMATH DE Number: 636046
zbMATH Keywords: nilpotent Lie algebras
zbMATH Keywords: Lie algebra
zbMATH Keywords: large deviation principle
zbMATH Keywords: nonlinear filtering
author: Toussaint Joseph Rabeherimanana
reviewed by: R. L. Schilling
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 636046