  In this paper, we consider the nonparametric estimation problem of the drift
function of stochastic differential equations driven by $\alpha$-stable
L\'{e}vy motion. First, the Kullback-Leibler divergence between the path
probabilities of two stochastic differential equations with different drift
functions is optimized. By using the Lagrangian multiplier, the variational
formula based on the stationary Fokker-Planck equation is constructed. Then
combined with the data information, the empirical distribution is used to
replace the stationary density, and the drift function is estimated
non-parametrically from the perspective of the process. In the numerical
experiment, the different amounts of data and different $\alpha$ values are
studied. The experimental results show that the estimation result of the drift
function is related to both. When the amount of data increases, the estimation
result will be better, and when the $\alpha$ value increases, the estimation
result is also better.
