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作者：Giraitis, L; Taqqu, MS; Terrin, N
作者单位：Vilnius University; Boston University; Tufts Medical Center
摘要：Let (X-t, t is an element of Z) be a linear sequence with non-Gaussian innovations and a spectral density which varies regularly at low frequencies. This includes situations, known as strong (or long-range) dependence, where the spectral density diverges at the origin. We study quadratic forms of bivariate Appell polynomials of the sequence (X-t) and provide general conditions for these quadratic forms, adequately normalized, to converge to a non-Gaussian distribution, We consider, in particul...
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作者：Zahle, M
作者单位：Friedrich Schiller University of Jena
摘要：The classical Lebesgue-Stieltjes integral integral(a)(b)f dg of real or complex-valued functions on a finite interval (a, b) is extended to a large class of integrands f and integrators g of unbounded variation. The key is to use composition formulas and integration-by-part rules for fractional integrals and Weyl derivatives. In the special case of Holder continuous functions f and g of summed order greater than 1 convergence of the corresponding Riemann-Stieltjes sums is proved. The results a...
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作者：Sun, YE
作者单位：National University of Singapore; Yale University
摘要：For a large collection of random variables in an ideal setting, pairwise independence is shown to be almost equivalent to mutual independence. An asymptotic interpretation of this fact shows the equivalence of asymptotic pairwise independence and asymptotic mutual independence for a triangular array (or a sequence) of random variables. Similar equivalence is also presented for uncorrelatedness and orthogonality as well as for the constancy of joint moment functions and exchangeability. General...
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作者：Toth, B; Werner, W
作者单位：HUN-REN; HUN-REN Alfred Renyi Institute of Mathematics; Hungarian Academy of Sciences; Universite Paris Saclay
摘要：We construct and study a continuous real-valued random process, which is of a new type: It is self-interacting (self-repelling) but only in a local sense: it only feels the self-repellance due to its occupation-time measure density in the 'immediate neighbourhood' of the point it is just visiting. We focus on the most natural process with these properties that we call 'true self-repelling motion'. This is the continuous counterpart to the integer-valued 'true' self-avoiding walk, which had bee...
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作者：Erdos, L
作者单位：New York University
摘要：We obtain the Lifschitz tail, i.e. the exact low energy asymptotics of the integrated density of states (IDS) of the two-dimensional magnetic Schrodinger operator with a uniform magnetic field and random Poissonian impurities. The single site potential is repulsive and it has a finite but nonzero range. We show that the IDS is a continuous function of the energy at the bottom of the spectrum. This result complements the earlier (nonrigorous) calculations by Brezin, Gross and Itzykson which pre...
