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Comment on “Fokker-Planck equations for nonlinear dynamical systems driven by non-Gaussian Lévy processes” [J. Math. Phys. 53, 072701 (2012)]
1.X. Sun and J. Duan, “Fokker-Planck equations for nonlinear dynamical systems driven by non-Gaussian Lévy processes,” J. Math. Phys. 53, 072701 (2012).
2.S. G. Krantz and H. R. Parks, A Primer of Real Analytic Functions, 2 ed. (Birkhäuser Advanced Texts Basler Lehrbücher, Birkhäuser Basel, 2012).
3.D. Applebaum, Lévy Processes and Stochastic Calculus (Cambridge University Press, Cambridge, 2004).
4.M. Magdziarz and T. Zorawik, “Stochastic representation of a fractional subdiffusion equation. The case of infinitely divisible waiting times, Lévy noise and space-time-dependent coefficients,” Proc. Am. Math. Soc. 144, 1767 (2015).
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In the proof of Theorem 1 in Sun and Duan [J. Math. Phys. 53, 072701 (2012)], the authors use the Taylor expansion to represent an arbitrary infinitely differentiable function with compact support, which is incorrect. We prove that although the derivation is incorrect, the statement of Theorem 1 remains valid if we add certain additional assumptions.
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