CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST 2008, 24(6) 561-573 DOI:      ISSN: 1001-4268 CN: 31-1256

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Keywords
Semimartingale
limit theorems
integrated error processes
convergence in law
stable convergence in law.
Authors
Xiao Xiaoqing
Xie Yingchao
PubMed
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Convergence Theorems of the Limit Processes of Integrated Errors of Semimartingale Sequence

Xiao Xiaoqing,Xie Yingchao

School of Science, Nantong University; School of Mathematical Sciences, Xuzhou Normal University

Abstract��

Jacod, Jakubowski and M\'emin studied the integrated error processes $Y^n(X)$ and $Z^{n,p}(X)$ which relates to the error process $^n\!X_t=X_t-X_{[nt]/n}$ for semimartingale $X$ with independent increments. And they also investigated the limit theorems for the semimartingale sequence $\{(Y(X^n),Z^p(X^n))\}_{n\ge 1}$. If denote the limit points of $\{(Y(X^n),Z^p(X^n))\}_{n\ge 1}$ by
$(Y(X),Z^p(X))$, Jacod et al. gave the formula of $(Y(X),Z^p(X))$. In this paper, we will investigate the convergence theorems of $Y(X^n)$ and $Z^{p}(X^n)$ for semimartingale sequence $\{X^n\}_{n\ge 1}$. We study mainly the convergence in law and the stable convergence in law of $\{(X^n,Y(X^n),Z^p(X^n))\}_{n\ge 1}$.

Keywords�� Semimartingale   limit theorems   integrated error processes   convergence in law   stable convergence in law.  
Received 1900-01-01 Revised 1900-01-01 Online:  
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Corresponding Authors: Xie Yingchao
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