On high-order discrete derivatives of stochastic variables

Aiazzi, 1999, IEEE Signal Processing Lett., 6, 138, 10.1109/97.763145 Chandramouli, 1999, IEEE Signal Processing Lett., 6, 129, 10.1109/97.763142 Karkuszewski, 2002, Phys. Rev. Lett., 89, 170405, 10.1103/PhysRevLett.89.170405 Moriya, 1993, Phys. Rev. Lett., 71, 883, 10.1103/PhysRevLett.71.883 Moriya, 1995, Phys. Rev. Lett., 75, 1981, 10.1103/PhysRevLett.75.1981 Faruqi, 2000, Appl. Math. Comput., 115, 213, 10.1016/S0096-3003(98)10068-1 Heald, 2000, Phys. Rev. Lett., 84, 2366, 10.1103/PhysRevLett.84.2366 Grewal, 1993 Wiener, 1923, J. Math. Phys. Sci., 2, 132 Dorogovtsev, 1994 Di Nunno, 2001, Pure Math., 12, 1 Kleinert, 1997, Phys. Lett. A, 235, 105, 10.1016/S0375-9601(97)00660-9 Elachi, 1980, Science, 209, 1073, 10.1126/science.209.4461.1073 Davis, 1976 Joshi, 1975 Kontorovich, 1996, IEEE Signal Processing Lett., 3, 19, 10.1109/97.475826 Kay, 1998, IEEE Signal Processing Lett., 5, 318, 10.1109/97.735424 Tribelsky, 2002, Phys. Rev. Lett., 89, 070201, 10.1103/PhysRevLett.89.070201 See for example the classical proof by K. Weierstrass, Mathematische Werke, Bd. III, Berlin 1903, pp. 1–17. Can also be found in most textbooks on Functional Analysis.