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A.A. Gushchin, Esko Valkeila

Approximations and limit theorems for likelihood ratio processes in the binary case

We study the asymptotic properties of the likelihood ratio processes for a sequence of binary filtered experiments. First we prove approximation results for the log-likelihood ratio processes and then apply them to obtain weak limit theorems. Here the limiting process is the stochastic exponential of a continuous martingale. Our results extend the corresponding results in the well-known monograph of Jacod and Shiryaev [16, Chapter X].

It turns out that the main results are valid for nonnegative supermartingales, too.

Statistics & Decisions, Oldenbourg Wissenschaftsverlag

Print ISSN: 0721-2631
Volume: 21, 03/2003
Pages: 219

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