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We treat the change point problem in ergodic diffusion processes fromdiscrete observations. Tonaki et al. (2020) proposed adaptive tests fordetecting changes in the diffusion and drift parameters in ergodic diffusionmodels. When any changes are detected by this method, the next question to beconsidered is where the change point is. Therefore, we propose the method toestimate the change point of the parameter for two cases: the case where thereis a change in the diffusion parameter, and the case where there is no changein the diffusion parameter but a change in the drift parameter. Furthermore, wepresent rates of convergence and distributional results of the change pointestimators. Some examples and simulation results are also given.

Estimation for change point of discretely observed ergodic diffusion processes