Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1156206 | Stochastic Processes and their Applications | 2008 | 43 Pages |
Abstract
This paper is concerned with the asymptotic behavior of sums of the form Un(f)t=∑i=1[t/Δn]f(XiΔn−X(i−1)Δn), where XX is a 1-dimensional semimartingale and ff a suitable test function, typically f(x)=|x|rf(x)=|x|r, as Δn→0Δn→0. We prove a variety of “laws of large numbers”, that is convergence in probability of Un(f)tUn(f)t, sometimes after normalization. We also exhibit in many cases the rate of convergence, as well as associated central limit theorems.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Jean Jacod,