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Глава

On an information-type inequality for the Hellinger process

P. 83-109.

Let X be a semimartingale which is locally square integrable and admitting the canonical decompositions X=M+A and X=M ' +A ' with respect to measures P and P ' . Let γ be the density of A-A ' with respect to C=(〈M〉+〈M ' 〉) in the Lebesgue decomposition. Then there is a version h of the Hellinger process h(1/2;P,P ' ) such that (1-Δh) -2 ·h⪰(1/8)γ 2 ·C P- and P ' -a.s. This inequality is related with a generalization of the Cramér-Rao inequality to the case of filtered space. The author gives some applications to a continuous-time linear regression model as well as to a discrete-time autoregression model with martingale errors.

В книге

Под науч. редакцией: S. Watanabe, M. Fukushima, Y. V. Prohorov et al. Singapore: World Scientific, 1996.