Abstract
AbstractWe propose an online parametric estimation method of stochastic differential equations with discrete observations and misspecified modelling based on online gradient descent. Our study provides uniform upper bounds for the risks of the estimators over a family of stochastic differential equations. Theoretical guarantees for the estimation of stochastic differential equations with discrete observations by online gradient descent are novel to our best knowledge.
Funder
Japan Society for the Promotion of Science
Japan Science and Technology Corporation
The University of Tokyo
Publisher
Springer Science and Business Media LLC
Reference38 articles.
1. Agarwal, A., Bartlett, P. L., Ravikumar, P., & Wainwright, M. J. (2012). Information-theoretic lower bounds on the oracle complexity of stochastic convex optimization. IEEE Transactions on Information Theory, 58(5), 3235–3249.
2. Bass, R. F., & Perkins, E. (2009). A new technique for proving uniqueness for martingale problems. Astérisque, 327, 47–53.
3. Bhudisaksang, T., & Cartea, A. (2021). Online drift estimation for jump-diffusion processes. Bernoulli, 27(4), 2494–2518.
4. Bibby, B. M., & Sørensen, M. (1995). Martingale estimation functions for discretely observed diffusion processes. Bernoulli, 1, 17–39.
5. De Gregorio, A., & Iacus, S. M. (2012). Adaptive LASSO-type estimation for multivariate diffusion processes. Econometric Theory, 28(4), 838–860.