A central limit theorem for the realized volatility of a one-dimensional continuous semimartingale based on a general stochastic sampling scheme is proved. The asymptotic distribution depends on the sampling scheme, which is written explicitly in terms of the asymptotic skewness and kurtosis of...

The present paper characterizes various properties of chaos processes which in particular include processes where all time variables admit a Wiener chaos expansion of a fixed finite order. The main focus is on the semimartingale property, p-variation and continuity. The general results obtained...

This paper presents limit theorems for certain functionals of semimartingales observed at high frequency. In particular, we extend results from Jacod (2008) [5] to the case of bipower variation, showing under standard assumptions that one obtains a limiting variable, which is in general...

The concept of selfdecomposability has been generalized to that of [alpha]-selfdecomposability, , by many authors. We first mention the existing results on the class of [alpha]-selfdecomposable distributions and investigate the remaining problems. We give complete characterizations by stochastic...

We consider the first passage percolation model on the lattice. In this model, we assign independently to each edge e a non-negative passage time t(e) with a common distribution F. Let a0,n be the passage time from the origin to (n,0,...,0). Under the exponential tail assumption, Kesten (1993)...

The two-parameter Poisson-Dirichlet distribution is the law of a sequence of decreasing nonnegative random variables with total sum one. It can be constructed from stable and gamma subordinators with the two parameters, [alpha] and [theta], corresponding to the stable component and the gamma...

By analogy with the theory of Backward Stochastic Differential Equations, we define Backward Stochastic Difference Equations on spaces related to discrete time, finite state processes. This paper considers these processes as constructions in their own right, not as approximations to the...

Itô's contributions lie at the root of stochastic calculus and of the theory of excursions. These ideas are also very useful in the study of conformally invariant two-dimensional structures, via conformal loop ensembles, excursions of Schramm-Loewner evolutions and Poisson point processes of...

We explain how Itô's excursion theory can be used to understand the asymptotic behavior of large random trees. We provide precise statements showing that the rescaled contour of a large Galton-Watson tree is asymptotically distributed according to Itô's excursion measure. As an application, we...

We consider the bifurcating Markov chain model introduced by Guyon to detect cellular aging from cell lineage. To take into account the possibility for a cell to die, we use an underlying super-critical binary Galton-Watson process to describe the evolution of the cell lineage. We give in this...