Nonlinear filtering of convex sets of probability distributions
type: Item
instance of: scholarly article
title: Nonlinear filtering of convex sets of probability distributions
zbMATH Open document ID: 1017.60047
DOI: 10.1016/S0378-3758(01)00207-5
author: R. Smith
published in: Journal of Statistical Planning and Inference
publication date: 2002-08-28T00:00:00Z
review text: The authors solve a filtering problem for a nonlinear dynamical system whose initial state is specified by a convex set of probability distributions (rather than a single distribution, such as the Gaussian distribution). The system is continuous-time and is observed in discrete time. The convex set of prior densities is defined as the set of (convex) mixtures generated by a given finite set of probability distributions, say \(\Pi\). Galerkin's method is used to solve Kolmogorov's equations for the posterior densities. Their means and variances are expressed by using the elements of \(\Pi\).
Mathematics Subject Classification ID: 60G35
Mathematics Subject Classification ID: 93E11
zbMATH DE Number: 1790203
zbMATH Keywords: imprecise probabilities
zbMATH Keywords: Kolmogorov's equations
zbMATH Keywords: Galerkin approximation
reviewed by: Georgi N. Boshnakov
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1790203