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Статья

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

Statistics & Decisions. 2003. Vol. 21. No. 3. P. 219-260.
Gushchin A. A., Valkeila E.

The authors study asymptotic properties of likelihood ratio processes for a sequence of binary filtered experiments by first obtaining an approximation for the log-likelihood ratio process and then applying it to obtain weak limit theorems. The limiting process is the stochastic exponential of a continuous martingale. The results obtained extend some results in Chapter 10 of [J. Jacod and A. N. Shiryaev, Limit theorems for stochastic processes, 2 nd ed. (2003; Zbl 1018.60002)].