  The problem of estimating a parameter in the drift coefficient is addressed
for $N$ discretely observed independent and identically distributed stochastic
differential equations (SDEs). This is done considering additional constraints,
wherein only public data can be published and used for inference. The concept
of local differential privacy (LDP) 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, and is some situations may be
completely different from the case where privacy constraints are ignored. Our
results hold true as the discretization step approaches zero and the number of
processes $N$ tends to infinity.
