Abstract

The problem of parameter drift estimation is addressed for $N$ discretely observed iid SDEs, considering the additional constraints that 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 aim 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 satisfy the privacy requirement. Our main results consist in deriving explicit conditions on the privacy level for which the associated estimator is proven to be consistent and in studying the asymptotic law of the estimator. These results are obtained under the assumption that the discretization step approaches zero and the number of processes $N$ tends to infinity. Joint work with Chiara Amorino - Universitat Pompeu Fabra (Barcelona) Helene Halconruy - TelecomSudParis (France)