We study the estimation problem for a continuous (Gaussian) process with independent increments when both the mean (drift) and variance (diffusion coefficient) are functions of the parameter [theta], in the situation where we cannot observe the whole path of the process but we are allowed to...

This paper studies conditions of tightness for sequences of processes, which conditions are mostly based on the use of 'dominating' increasing processes. The results obtained follow in directions initiated by Aldous and Rebolledo and are particularly well-suited for studying sequences of...

This paper presents a generalized pre-averaging approach for estimating the integrated volatility, in the presence of noise. This approach also provides consistent estimators of other powers of volatility -- in particular, it gives feasible ways to consistently estimate the asymptotic variance...

In this paper we extend the notion of Hellinger processes, which was known for pairs of probability measures defined on a filtered space, to general filtered statistical experiments. In a sense, this notion generalizes the Mellin transforms of a (nonfiltered) statistical experiment. Then we...

In Jacod (1989) we have introduced the family of Hellinger processes associated with a filtered statistical experiment. Here we are concerned with the (weak) convergence of such experiments, expressed in terms of their Hellinger processes, in the case where the limiting experiment has...

We introduce a notion of partial likelihood for binary statistical experiments, when the relevant observation consists of a stochastic process which is a semimartingale with prescribed characteristics. This extends the concept of partial likelihood introduced by Cox. We also present a notion of...

This paper is concerned with the asymptotic behavior of sums of the form , where X is a 1-dimensional semimartingale and f a suitable test function, typically f(x)=xr, as [Delta]n--0. We prove a variety of "laws of large numbers", that is convergence in probability of Un(f)t, sometimes after...

We derive Central Limit Theorems for the convergence of approximate quadratic variations, computed on the basis of regularly spaced observation times of the underlying process, toward the true quadratic variation. This problem was solved in the case of an Itô semimartingale having a...