The nisio semigroup for controlled diffusions with partial observations

Borkar, Vivek S. (1986) The nisio semigroup for controlled diffusions with partial observations Stochastics, 17 (1-2). pp. 145-160. ISSN 1744-2508

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A one parameter semigroup of nonlinear operators on an appropriate Banach space is constructed in the spirit of Nisio for controlled diffusions with partial observations. The method is based upon considering an equivalent problem of controlling a measure-valued process representing the conditional law of the state given past observations. The latter evolves according to the usual equations of nonlinear filtering. By considering an appropriate augmentation of the class of controls, it is shown that the "minimum cost" operators associated with this control problem indeed form a semigroup of nonlinear contractions on the space of bounded continuous real-valued functions on the state space of the above measure-valued process.

Item Type:Article
Source:Copyright of this article belongs to Taylor and Francis Group.
Keywords:Nonlinear Semigroups; Partial Observations; Optimal Control; Non-Linear Filtering; Measure-Valued Process
ID Code:81420
Deposited On:06 Feb 2012 04:30
Last Modified:06 Feb 2012 04:30

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