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Papers by Assane Diop

Research paper thumbnail of Sur la convergence de certaines fonctionnelles de semimartingales discrétisées

Research paper thumbnail of Central Limit Theorem for Approximate Quadratic Variations of Pure Jump Itô Semimartingales ∗ Forthcoming in Stochastic Processes and their Applications

We derive Central Limit Theorems for the convergence of approximate quadratic variations, compute... more 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 non-vanishing continuous martingale part. Here we focus on the case where the continuous martingale part vanishes and find faster rates of convergence, as well as very different limiting processes. AMS 2000 subject classifications: 60F05, 60F17, 60G51, 60G07.

Research paper thumbnail of Convergence of some random functionals of discretized semimartingales

Bernoulli, 2012

In this paper, we study the asymptotic behavior of sums of functions of the increments of a given... more In this paper, we study the asymptotic behavior of sums of functions of the increments of a given semimartingale, taken along a regular grid whose mesh goes to 0. The function of the ith increment may depend on the current time, and also on the past of the semimartingale before this time. We study the convergence in probability of two types of such sums, and we also give associated central limit theorems. This extends known results when the summands are a function depending only on the increments, and this is motivated mainly by statistical applications.

Research paper thumbnail of Sur la convergence de certaines fonctionnelles de semimartingales discrétisées

Research paper thumbnail of Central Limit Theorem for Approximate Quadratic Variations of Pure Jump Itô Semimartingales ∗ Forthcoming in Stochastic Processes and their Applications

We derive Central Limit Theorems for the convergence of approximate quadratic variations, compute... more 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 non-vanishing continuous martingale part. Here we focus on the case where the continuous martingale part vanishes and find faster rates of convergence, as well as very different limiting processes. AMS 2000 subject classifications: 60F05, 60F17, 60G51, 60G07.

Research paper thumbnail of Convergence of some random functionals of discretized semimartingales

Bernoulli, 2012

In this paper, we study the asymptotic behavior of sums of functions of the increments of a given... more In this paper, we study the asymptotic behavior of sums of functions of the increments of a given semimartingale, taken along a regular grid whose mesh goes to 0. The function of the ith increment may depend on the current time, and also on the past of the semimartingale before this time. We study the convergence in probability of two types of such sums, and we also give associated central limit theorems. This extends known results when the summands are a function depending only on the increments, and this is motivated mainly by statistical applications.

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