In this paper, we consider the problem of parameter estimation for a real stochastic model observed at some discrete times, that is a solution of a stochastic differential equation driven by \(\alpha\) -stable processes, \(\alpha \in (1,2)\) . After recalling the non-parametric estimation framework of the drift function namely the Nadaraya-Watson estimation, we provide explicit estimators for the diffusion parameters (the scaling and the driving stable process parameters) based on the Euler-Maruyama scheme. We apply the estimation results to stable driven Ornstein-Uhlenbeck (OU), Cox-Ingersoll-Ross (CIR) and Lotka-Volterra processes. We also consider the estimation of the drift coefficients in the linear case namely, the stable driven OU and CIR processes. The novelty of this paper which is our baseline is the combination of a characteristic sample function method, the least squares or linear statistical regression methods and the Itô formula. We also established under certain conditions, the consistency of their drift coefficient estimators of the stable driven OU and CIR processes. We efficiently discuss our result with numerical simulations using synthetic data. A real data in finance, such as exchange rates is used to fit the parameters of a justified model among the above stable driven processes. As a forthcoming work, we intend to study the rate of convergence of the estimators and to create a package on R software to handle this kind of estimation problem. We are also currently interested in ergodicity properties for a class of stochastic differential equations driven by stable processes.
