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In this paper, we consider the nonparametric estimation problem of the driftfunction of stochastic differential equations driven by $\alpha$-stableL\'{e}vy motion. First, the Kullback-Leibler divergence between the pathprobabilities of two stochastic differential equations with different driftfunctions is optimized. By using the Lagrangian multiplier, the variationalformula based on the stationary Fokker-Planck equation is constructed. Thencombined with the data information, the empirical distribution is used toreplace the stationary density, and the drift function is estimatednon-parametrically from the perspective of the process. In the numericalexperiment, the different amounts of data and different $\alpha$ values arestudied. The experimental results show that the estimation result of the driftfunction is related to both. When the amount of data increases, the estimationresult will be better, and when the $\alpha$ value increases, the estimationresult is also better.

Variational inference of the drift function for stochastic differential equations driven by L\'{e}vy processes