We treat the change point problem in ergodic diffusion processes from discrete observations. Tonaki et al. (2020) proposed adaptive tests for detecting changes in the diffusion and drift parameters in ergodic diffusion models. When any changes are detected by this method, the next question to be considered is where the change point is. Therefore, we propose the method to estimate the change point of the parameter for two cases: the case where there is a change in the diffusion parameter, and the case where there is no change in the diffusion parameter but a change in the drift parameter. Furthermore, we present rates of convergence and distributional results of the change point estimators. Some examples and simulation results are also given.
翻译:我们从离散观测中从离散观测中处理异地扩散过程中的变化点问题。Tonaki等人(2020年)提议进行适应性测试,以检测异地扩散模型中扩散和漂移参数的变化。如果通过这种方法检测到任何变化,下一个要考虑的问题是变化点在哪里。因此,我们提议了两种情况参数变化点的估计方法:扩散参数发生变化的情况,以及扩散参数没有变化但漂移参数发生变化的情况。此外,我们提出了变化点估计器的趋同率和分布结果,还给出了一些实例和模拟结果。