摘要翻译：
假定一维扩散过程$x=\{X_t,0\leq t\leq t\}$,其漂移量$b(x)$和扩散系数$\sigma(\theta,x)=\sqrt{\theta}\sigma(x)$已知到$\theta>0$,在(0，t)$中的某个点$t^*\转换波动机制。在从$x$的离散时间观测的基础上，问题是估计波动率结构$t^*$变化的瞬间，以及在变化点之前和之后的两个值$theta$，例如$theta_1$和$theta_2$。假定采样以规则间隔的时间间隔进行，间隔长度为$\delta_n$，且$n\delta_n=t$。为了解决我们的统计问题，我们使用最小二乘法。在高频格式下给出了估计量的相合性、收敛速度和分布结果。我们还研究了具有未知漂移和未知波动但常数的扩散过程的情形。
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英文标题：
《Least squares volatility change point estimation for partially observed
  diffusion processes》
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作者：
A. De Gregorio, S.M. Iacus
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最新提交年份：
2007
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分类信息：

一级分类：Mathematics        数学
二级分类：Statistics Theory        统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Mathematics        数学
二级分类：Probability        概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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一级分类：Statistics        统计学
二级分类：Applications        应用程序
分类描述：Biology, Education, Epidemiology, Engineering, Environmental Sciences, Medical, Physical Sciences, Quality Control, Social Sciences
生物学，教育学，流行病学，工程学，环境科学，医学，物理科学，质量控制，社会科学
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一级分类：Statistics        统计学
二级分类：Statistics Theory        统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
  A one dimensional diffusion process $X=\{X_t, 0\leq t \leq T\}$, with drift $b(x)$ and diffusion coefficient $\sigma(\theta, x)=\sqrt{\theta} \sigma(x)$ known up to $\theta>0$, is supposed to switch volatility regime at some point $t^*\in (0,T)$. On the basis of discrete time observations from $X$, the problem is the one of estimating the instant of change in the volatility structure $t^*$ as well as the two values of $\theta$, say $\theta_1$ and $\theta_2$, before and after the change point. It is assumed that the sampling occurs at regularly spaced times intervals of length $\Delta_n$ with $n\Delta_n=T$. To work out our statistical problem we use a least squares approach. Consistency, rates of convergence and distributional results of the estimators are presented under an high frequency scheme. We also study the case of a diffusion process with unknown drift and unknown volatility but constant.
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PDF链接：
https://arxiv.org/pdf/709.2967