2010/01/13 by Assane Diop, Diop, Assane
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability #Probability (math.PR) #Probability and Risk Models #Stochastic processes and financial applications #math.PR
paper · pdf · doi:10.48550/arxiv.1001.2182
31 pages
arxiv created 2010/01/13 · openalex publication_date 2010/01/13 · arxiv updated 2010/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.