A Generalized Occupation Time Formula For Continuous Semimartingales

Raouf Ghomrasni

A Generalized Occupation Time Formula For Continuous Semimartingales

概率论 2007-05-23 v1

作者: Raouf Ghomrasni

摘要

We show that for a wide class of functions $F$ that: ${\lim_{\epsilon \downarrow 0} {\frac{1}{\epsilon}} \int_0^t \Big\{F(s, X_s) - F(s, X_s - \epsilon)\Big\} d\big<X,X\big>_s} = - \int_0^t\int_{\R} F(s, x) d L_s^x$ where $X_t$ is a continuous semi-martingale, $(L_t^x, x \in \R, t \geq 0)$ its local time process and $(\big<X,X\big>_t, t \geq 0)$ its quadratic variation process.

关键词

martingale theory fourier analysis function theory

引用

@article{arxiv.math/0612699,
  title  = {A Generalized Occupation Time Formula For Continuous Semimartingales},
  author = {Raouf Ghomrasni},
  journal= {arXiv preprint arXiv:math/0612699},
  year   = {2007}
}

备注

3 pages

相关论文

查看更多相关论文 →