A Representation Theorem on a Filtering Model with First-Passage-Type Stopping Time
Vol. 23 (2016), No. 2, Page 529–568.
Nakashima, Takenobu
A Representation Theorem on a Filtering Model with First-Passage-Type Stopping Time
[Full Article (PDF)] [MathSciNet Review (HTML)] [MathSciNet Review (PDF)]
Abstract:
We present a representation theorem for a filtering model with first-passage-type stopping time. The model is constructed from two unobservable processes and one observable process that is under the influence of two unobservable processes. A filter is constructed using Brownian motion in the observable process and a first-passage-type stopping time in an unobservable process. Though our theorems are similar to those of Nakagawa\cite{Nakagawa}, we do not use pinned Brownian motion measure, which is difficult to deal with. In addition, we describe a representation theorem for another filtration that was not discussed by Nakagawa\cite{Nakagawa}.
Keywords: Information, hazard process of default time, intensity, filtration.
Mathematical Reviews Number: MR3469008
Received: 2014-11-17
