Maximum likelihood estimation for multiscale Ornstein-Uhlenbeck processes

作者：Zhang, Fan; Papavasiliou, Anastasia^*

来源：Stochastics-An International Journal of Probability and Stochastic Reports, 2018, 90(6): 807-835.

DOI：10.1080/17442508.2018.1424853

• Multiscale diffusions
• Ornstein-Uhlenbeck process
• parameter estimation
• maximum likelihood
• subsampling

We study the problem of estimating the parameters of an Ornstein-Uhlenbeck (OU) process that is the coarse-grained limit of a multiscale system of OU processes, given data from the multiscale system. We consider both the averaging and homogenization cases and both drift and diffusion coefficients. By restricting ourselves to the OU system, we are able to substantially improve the results with strong modes of convergence, and provide some intuition of what to expect in the general case. In particular, in the homogenisation case we derive optimal rates of sub-sampling to minimize the estimation errors.

• 出版日期2018
• 单位对外经济贸易大学