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

Alexander Gushchin and Valkeila Esko

Statistics & Risk Modeling, 2003, vol. 21, issue 3, 219-260

Abstract: 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.

Date: 2003
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DOI: 10.1524/stnd.21.3.219.23429

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