  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. The derivation
of the bounds involves three underlying theoretical results: the analysis of
the stochastic mirror descent algorithm based on dependent and biased
subgradients, the simultaneous exponential ergodicity of classes of diffusion
processes, and the proposal of loss functions whose approximated stochastic
subgradients are dependent only on the known model and observations.
