Limit Distributions for Sums of Independent Random Vectors: Heavy Tails in Theory and Practice

By Hans-Peter Scheffler, Mark M. Meerschaert. 2001

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Citations in the corpus

Operator scaling stable random fields (2006, background): “4 of [16] that for any δ > 0 there exists a constant C > 0 such that ‖r E t θ‖0 ≤ Cra1−δ for all 0 < r ≤ 1 and θ ∈ S0.”
Precise large deviations for sums of random variables with consistently varying tails (2004, background): “For more details on heavy-tailed distributions please refer to Embrechts et al. (1997) and Meerschaert and Scheffler (2001).”
Brownian subordinators and fractional Cauchy problems (2007, background): “This means that X0(ct) and cX0(t) are identically distributed for all c > 0, for some linear operator E; see, for example, [34, 37].”
VECTOR GRÜNWALD FORMULA FOR FRACTIONAL DERIVATIVES (2004, methodology): “The argument is similar to the case 1 < α < 2 proved in [17], Lemma 7.”
REGULAR VARIATION FOR MEASURES ON METRIC SPACES (2006, background): “[22], [19]), of componentwise partial maxima and point processes (extreme value theory, see e.”
SDEs Driven by a Time-Changed Lévy Process and Their Associated Time-Fractional Order Pseudo-Differential Equations (2009, background): “rder time derivative on the left side of equation (1.1) is replacedby atime-fractionalorderderivative,hasappearedin the framework of continuous time random walks (CTRWs) and fractional kinetic theory [5,9, 17,19,20,31]. Papers [7,18,27,29] establish that time-fractional versions of the Cauchy proble”
Integral representations and properties of operator fractional Brownian motions (2011, background): “Becker-Kern and Pap [2] consider estimation of the real spectrum of the self-similarity exponent. A number of other works on operator self-similarity are naturally related to OFBMs; see, for example, [28], Section 11, and references therein. To the reader less familiar with OFBMs, we should note tha”
Space-time fractional diffusion on bounded domains (2011, background): “≥ 0} converges weakly to a rotationally symmetric α-stable L´evy motion {At,t≥ 0} with E[eiξ·At] = e−C0 |ξ αt for every ξ∈ Rd and t≥ 0, where the constant C0 depends only on Cand the dimension d, see [18]. A simple rescaling in space yields a standard stable process with C0 = 1. Since {λ1/αAt,t≥ 0} ”
Triangular array limits for continuous time random walks (2008, background): “A multivariable theory of regular variation is developed in [37], and applications to finance are suggested in [7,38].”
A second-order accurate numerical method for the two-dimensional fractional diffusion equation (2007, background): “A more complicated form that mixes the two orders a and b of fractional differentiation pertains if the diffusing particle makes x and y jumps that are not statistically independent [3,18,19].”