White noise calculus and nonlinear filtering theory
type: Item
instance of: scholarly article
title: White noise calculus and nonlinear filtering theory
zbMATH Open document ID: 0584.60055
author: Gopinath Kallianpur
author: Rajeeva L. Karandikar
published in: The Annals of Probability
publication date: 1985-01-01T00:00:00Z
review text: Quite a while ago, \textit{A. V. Balakrishnan} stressed the inadequacies of modeling white noise with a Wiener process [see for example, Appl. Math. Optimization 1, 97-120 (1974; Zbl 0306.90056)] and suggested that white noise be represented by an additive only probability measure. His main concern was the problem of detecting signals. The present authors have been working for a while with the same additive model, but with an emphasis on the problem of filtering signals (see the bibliography of the paper being reviewed). They give here an overview of their work. To be brief, the conclusion is that, ''mutatis mutandis'', the same results can be obtained whether the noise is modeled as a Wiener process or as an additive only probability, but that, to reach that conclusion, much mathematics must be produced!
Mathematics Subject Classification ID: 60G35
Mathematics Subject Classification ID: 60A05
Mathematics Subject Classification ID: 60H15
Mathematics Subject Classification ID: 93E11
zbMATH DE Number: 3936114
zbMATH Keywords: nonlinear filtering
zbMATH Keywords: white noise
zbMATH Keywords: finitely additive
zbMATH Keywords: likelihood ratios
zbMATH Keywords: robustness
zbMATH Keywords: consistency
reviewed by: A. F. Gualtierotti
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176992798
OpenAlex ID: W2019314142
DOI: 10.1214/AOP/1176992798
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description: scientific article; zbMATH DE number 3936114