积分伊藤过程平方差之和的极限定理及其在逆散射中的应用
概率论
2013-08-14 v3 光学
摘要
我们研究了一个泛函，该泛函通过对伊藤过程积分在不相交区间上的平方差求和得到。该和的极限被证明依概率收敛于底层过程二次变差的三分之二。给出了在随机分形表面逆散射中的应用。
引用
@article{arxiv.1211.6413,
title = {A limit theorem for the sum of squared differences of an integrated Ito process with application to inverse scattering},
author = {John F. A. Fletcher},
journal= {arXiv preprint arXiv:1211.6413},
year = {2013}
}
备注
This paper has been withdrawn by the author due to the discovery of an error in the first paragraph on p.4 (which has a serious effect on the subsequent argument). The statement beginning "Clearly..." is not in fact true in general (clearly)