Bibliography

The TME method is due to Dacunha-Castelle and Florens-Zmirou (1986); Florens-Zmirou (1989), where they use it to estimate diffusion processes coefficients.

It is also shown by Zhao et al. (2020) and Zhao (2021) that TME can be used in Gaussian filtering and smoothering, as well as deep GP regression problems.

• Didier Dacunha-Castelle and Danielle Florens-Zmirou. Estimation of the coefficients of a diffusion from discrete observations. Stochastics, 19(4):263–284, 1986.

• Danielle Florens-Zmirou. Approximate discrete-time schemes for statistics of diffusion processes. Statistics, 20(4):547–557, 1989.

• Mathieu Kessler. Estimation of an ergodic diffusion from discrete observations. Scandinavian Journal of Statistics, 24(2):211-229, 1997.

• Zheng Zhao. State-space deep Gaussian processes. PhD thesis, Aalto University, 2021. [PDF]

• Zheng Zhao and Simo Särkkä. Non-linear Gaussian smoothing with Taylor moment expansion. IEEE Signal Processing Letters, 2021.

• Zheng Zhao, Toni Karvonen, Roland Hostettler, and Simo Särkkä. Taylor moment expansion for continuous-discrete Gaussian filtering. IEEE Transactions on Automatic Control, 66(9):4460-4467, 2021. [DOI]