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作者：Hu, YZ; Nualart, D
作者单位：University of Kansas; University of Barcelona
摘要：Let B-t(H) H be a d-dimensional fractional Brownian motion with Hurst parameter H E (0, 1). Assume d ≥ 2. We prove that the renormalized self-intersection local time L = ∫(T)(0) ∫(t)(0) δ(B-t(H) - B-s(H)) ds dt - E(∫(T)(0) ∫(t)(0) δ(B-t(H) -B-s(H)) ds dt) exists in L-2 if and only if H < 3/(2d), which generalizes the Varadhan renormalization theorem to any dimension and with any Hurst parameter. Motivated by a result of Yor, we show that in the case 3/4 > H ≥ 3/2d, r(ε)Lε converges i...
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作者：Khoshnevisan, D; Xiao, YM
作者单位：Utah System of Higher Education; University of Utah; Michigan State University
摘要：We use the recently-developed multiparameter theory of additive Levy processes to establish novel connections between an arbitrary Levy process X in R-d, and a new class of energy forms and their corresponding capacities. We then apply these connections to solve two long-standing problems in the folklore of the theory of Levy processes. First, we compute the Hausdorff dimension of the image X(G) of a nonrandorn linear Borel set G subset of R+, where X is all arbitrary Levy process in Rd. Our w...
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作者：Xia, C
作者单位：University of Tennessee System; University of Tennessee Knoxville
摘要：Let S-1 (n), . . ., S-p(n) be independent symmetric random walks in Z(d). We establish moderate deviations and law of the iterated logarithm for the intersection of the ranges #{S-1[0, n] boolean AND . . . boolean AND S-p[0, n]} in the case d = 2, p >= 2 and the case d = 3, p = 2.
