We 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.
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Shogo H. Nakakita (2024) studied this question.
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