Comment on 'Fokker-Planck equations for nonlinear dynamical systems driven by non-Gaussian L\'evy processes' [J. Math. Phys. 53, 072701 (2012)]

摘要

In an article [J. Math. Phys. 53, 072701 (2012)] X. Sun and J. Duan presentedFokker-Planck equations for nonlinear stochastic differential equations withnon-Gaussian L\'evy processes. In this comment we show a serious drawback inthe derivation of their main result. In the proof of Theorem 1 in theaforementioned paper, a false assumption that each infinitely differentiablefunction with compact support is equal to its Taylor series, is used. We provethat although the derivation is incorrect, the result remains valid only if weadd certain additional assumptions.