Limit Distributions for Sums of Independent Random Vectors

By R. Feldman. 2002

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SDEs Driven by a Time-Changed Lévy Process and Their Associated Time-Fractional Order Pseudo-Differential Equations (2009, background): “1) is replaced by a time-fractional order derivative, has appeared in the framework of continuous time random walks (CTRWs) and fractional kinetic theory [5,9, 17,19,20,31].”
On Large Deviations of Sums of Independent Random Variables (2007, methodology): “This follows from the proof of Theorems 1 and 2 of §42 in Gnedenko and Kolmogorov (1968) with some modification, by using (3.”
Nonparametric estimation for L\'evy processes from low-frequency observations (2007, background): “Writing µn =⇒ µ for weak convergence of the finite Borel measures µn to the finite Borel measure µ on (R,B), the following well-known result will be essential in the sequel (Theorem VII.2.9 and Remark VII.2.10 in Jacod and Shiryaev (2002) or Theorem 19.1 in Gnedenko and Kolmogorov (1968)).”
Gaussian approximation of multivariate Lévy processes with applications to simulation of tempered stable processes (2007, background): “A comprehensive introduction to operator stable laws can be found in the monographs [7] and [12].”
Characterizations and Examples of Hidden Regular Variation (2004, unknown): “See Balkema (1973), Basrak et al. (2002), Davis and Hsing (1995), Davis and Mikosch (1998), de Haan et al. (1984), Meerschaert and Scheﬄer (2001), Resnick (1986), Resnick (1987, Chapter 5).”