The problem of estimating parameter drift is addressed for $N$ discretely observed independent and identically distributed SDEs. This is done considering additional constraints, wherein only privatized data can be published and used for inference. The concept of local differential privacy is formally introduced for a system of stochastic differential equations. The objective is to estimate the drift parameter by proposing a contrast function based on a pseudo-likelihood approach. A suitably scaled Laplace noise is incorporated to meet the privacy requirements. Our key findings encompass the derivation of explicit conditions tied to the privacy level. Under these conditions, we establish the consistency and asymptotic normality of the associated estimator. Notably, the convergence rate is intricately linked to the privacy level, marking a significant novelty in our results. This holds true as the discretization step approaches zero and the number of processes $N$ tends to infinity.

The talk is based on joint work with A. Gloter and H. Halconruy.