2006/04/20 by Jean Jacod, Jacod, Jean · 1 citation
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #60F17 #60G48 #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Probability and Risk Models #Stochastic processes and financial applications #math.PR #msc:60F17 #msc:60G48
paper · pdf · doi:10.48550/arxiv.math/0604450
arxiv created 2006/04/20 · openalex publication_date 2006/04/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper is concerned with the asymptotic behavior of sums of terms which are a test function f evaluated at successive increments of a discretely sampled semimartingale. Typically the test function is a power function (when the power is 2 we get the realized quadratic variation) . We prove a variety of ``laws of large numbers'', that is convergence in probability of these sums, sometimes after normalization. We also exhibit in many cases the rate of convergence, as well as associated central limit theorems.