On a posterior information process for parametric families of experiments

In a filtered statistical experiment a priori and a posteriori probability measures are defined on an abstract parametric space. The information in the posterior, given the prior, is defined by the usual Kullback-Leibler formula. Certain properties of this quantity is investigated in the context of so-called arithmetic and geometric measures and arithmetic and geometric processes. Interesting multiplicative decompositions are presented that involve Hellinger processes indexed both by prior and by posterior distributions

Information processes in filtered experiments

In this paper we give explicit representations for Kullback-Leibler information numbers between a priori and a posteriori distributions, when the observations come from a semimartingale. We assume that the distribution of the observed semimartingale is described in terms of the so-called triplet of predictable characteristics. We end by considering the corresponding notions in a model with a fractional noise

Arbitrage with fractional brownian motion?

In recent years fractional Brownian motion has been suggested to replace the classical Brownian motion as driving process in the modelling of many real world phenomena, including stock price modelling. In several papers seemingly contradictory results on the existence or absence of a riskless gain (arbitrage) in such stock models have been stated. This survey tries to clarify this issue by pointing to the importance of the chosen class of admissible trading strategies