Some recent results in finitely additive white noise theory
type: Item
instance of: scholarly article
title: Some recent results in finitely additive white noise theory
zbMATH Open document ID: 0820.60027
DOI: 10.1007/BF00994910
author: Arunabha Bagchi
author: Ravi R. Mazumdar
published in: Acta Applicandae Mathematicae
publication date: 1994-10-13T00:00:00Z
review text: This is mostly a review paper in which the authors describe results which they have obtained on the subject of finitely additive white noise theory, extending work of \textit{A. V. Balakrishnan} [see, for instance, ``Applied functional analysis'' (1976; Zbl 0333.93051)], and \textit{G. Kallianpur} and \textit{R. L. Karandikar} [see, for instance, ``White noise theory of filtering, prediction and smoothing'' (1988; Zbl 0724.93076)]. Most details are on the definition of conditional expectations, and a result on the representation of a nonlinear filter under the so-called Beneš condition is given. For related information see the paper reviewed above.
Mathematics Subject Classification ID: 60G35
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 93E11
zbMATH DE Number: 627450
zbMATH Keywords: nonlinear filter under the so-called Benes condition
zbMATH Keywords: finitely additive white noise theory
reviewed by: A. F. Gualtierotti
MaRDI profile type: Publication
cites work: White noise theory of robust nonlinear filtering with correlated state and observation noises
cites work: On Radon-Nikodym derivatives of finitely-additive measures induced by nonlinear transformations on hilbert space
cites work: Q3909518
cites work: Exact finite-dimensional filters for certain diffusions with nonlinear drift
cites work: Q4146134
cites work: The Transformation of Wiener Integrals by Nonlinear Transformations
cites work: Q3969647
cites work: A Radon-Nikodym theorem for finitely additive set functions
cites work: Integration and Nonlinear Transformations In Hilbert Space
cites work: Q3746598
cites work: Q3908216
cites work: Q3999268
cites work: White noise in atmospheric optics
cites work: Boundary value problems for stochastic differential equations
cites work: A Weierstrass theorem for real, separable Hilbert spaces
cites work: Q3240992
cites work: On nonlinear transformations of Gaussian measures
cites work: Q3334692
cites work: Riemann-Stieltjes approximations of stochastic integrals
full work available at URL: https://doi.org/10.1007/bf00994910
OpenAlex ID: W1994227200
description: scientific article; zbMATH DE number 627450