2015/09/08 by Takenobu Nakashima, Nakashima, Takenobu
Mathematics · #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1509.02304
We present a representation theorem for a filtering model with\nfirst-passage-type stopping time. The model is constructed from two\nunobservable processes and one observable process that is under the influence\nof two unobservable processes.A filter is constructed using Brownian motion in\nthe observable process and a first-passage-type stopping time in an\nunobservable process.Though our theorems are similar to those of\nNakagawa citeNakagawa, we do not use pinned Brownian motion measure, which is\ndifficult to deal with. In addition, we describe a representation theorem for\nanother filtration that was not discussed by Nakagawa\n