On an information-type inequality for the Hellinger process
- Gushchin, Alexander A.
2010 Mathematics Subject Classification
- 60G07 60G48
- semimartingale, Hellinger process, Cramér-Rao inequality, linear regression
Let (Ω,𝓕,𝔽) be a filtered space with two probability measures P and P' on (Ω,𝓕). Let X be a d-dimensional locally square-integrable semimartingale relative to P and P' with the canonical decomposition X = X0 + M + A and X = X0 + M' + A' respectively. We give a lower bound for the Hellinger process h(1⁄2; P, P') of order 1/2 between P and P' in terms of A, A' and the quadratic characteristic of M and M'. This result implies simple sufficient conditions for the entire separation of measures in a linear regression model with martingale errors.