分数扩散型过程的最佳顺序变化检测
Optimal sequential change-detection for fractional diffusion-type processes
摘要：
本文研究了连续观测随机过程的分布突变的检测问题。我们建立的最优性的CRACUUM测试相对于一个修改版本的Lorden的标准为任意过程的连续路径，并将此一般结果的特殊情况下的分数扩散型过程。作为一个副产品，我们表明，当分数布朗运动与赫斯特指数H采用多项式漂移项与指数H + 1/2的变化后，优化Lorden的原始标准的ESTUM测试。
英文摘要：
We consider the problem of detecting an abrupt change in the distribution of a sequentially observed stochastic process. We establish the optimality of the CUSUM test with respect to a modified version of Lorden's criterion for arbitrary processes with continuous paths and apply this general result to the special case of fractional diffusion-type processes. As a by-product, we show that the CUSUM test optimizes Lorden's original criterion when a fractional Brownian motion with Hurst index H adopts a polynomial drift term with exponent H + 1/2 after the change.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
