Nonlinear semigroup for the unnormalized conditional density
type: Item
instance of: scholarly article
title: Nonlinear semigroup for the unnormalized conditional density
zbMATH Open document ID: 0574.93065
author: Yasuhiro Fujita
published in: Tôhoku Mathematical Journal. Second Series
publication date: 1984-01-01T00:00:00Z
review text: The paper is concerned with the following partially observable control problems; the state process \(X_ t\) and the observation process \(Y_ t\) are governed by stochastic differential equations \[ dX_ t=b(X_ t,U_ t)dt+\sigma (X_ t)dW_ t,\quad dY_ t=h(X_ t)dt+d\tilde W_ t \] where \(U_ t\) is an admissible control. The author shows the regularity of the unnormalized conditional probability density, under some mild conditions, and constructs a nonlinear semigroup whose generator is related to the Mortensen equation.
Mathematics Subject Classification ID: 93E20
Mathematics Subject Classification ID: 47H20
Mathematics Subject Classification ID: 60H15
Mathematics Subject Classification ID: 49J55
zbMATH DE Number: 3918240
zbMATH Keywords: partially observable control problems
zbMATH Keywords: unnormalized conditional probability density
zbMATH Keywords: nonlinear semigroup
zbMATH Keywords: Mortensen equation
reviewed by: Makiko Nisio
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1178228682
OpenAlex ID: W1999443703
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DOI: 10.2748/TMJ/1178228682
description: scientific article; zbMATH DE number 3918240