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

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  • Gushchin A. A.
  • Valkeila Esko

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.

Suggested Citation

  • Gushchin A. A. & Valkeila Esko, 2003. "Approximations and limit theorems for likelihood ratio processes in the binary case," Statistics & Risk Modeling, De Gruyter, vol. 21(3), pages 219-260, March.
    • Handle: RePEc:bpj:strimo:v:21:y:2003:i:3/2003:p:219-260:n:3
    DOI: 10.1524/stnd.21.3.219.23429
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    Cited by:

    1. Alexander Gushchin & Nino Kordzakhia & Alexander Novikov, 2018. "Translation invariant statistical experiments with independent increments," Statistical Inference for Stochastic Processes, Springer, vol. 21(2), pages 363-383, July.

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