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作者：Takeda, M; Zhang, TS
作者单位：University of Osaka; University of Bielefeld
摘要：In this paper we study the asymptotic behavior of additive functionals of Brownian motion which are not necessarily of bounded variation. The result is then applied to the Hilbert transform of the Brownian local time.
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作者：Fitzsimmons, PJ
作者单位：University of California System; University of California San Diego
摘要：Let X and Y be symmetric diffusion processes with a common state space, and let P-m (resp. Q(mu)) be the law of X (resp. Y) with its symmetry measure m (resp. mu) as initial distribution. We study the consequences of the absolute continuity condition Q(mu) much less than loc P-m. We show that under this condition there is a smooth version rho of the Radon-Nikodym derivative d(mu)/dm such that 1/2[log rho(X-t) - log rho(X-0)] = M-t + N-t, t < sigma, where M is a continuous local martingale addi...
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作者：Peligrad, M; Utev, S
作者单位：University System of Ohio; University of Cincinnati; La Trobe University; Russian Academy of Sciences
摘要：In this paper we study the CLT for partial sums of a generalized linear process X-n = Sigma(i=1)(n) a(ni)xi(i), where sup(n) Sigma(i=1)(n) a(ni)(2) < infinity, max(1 less than or equal to i less than or equal to n)\a(ni)\ --> 0 as n --> infinity and xi(i)'s are in turn, pairwise mixing martingale differences, mixing sequences or associated sequences. The results are important in analyzing the asymptotical properties of some estimators as well as of linear processes.
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作者：Ho, HC; Hsing, T
作者单位：Academia Sinica - Taiwan; Texas A&M University System; Texas A&M University College Station
摘要：Let X-n = Sigma(i=1)(infinity) alpha(i) epsilon(n-i), where the epsilon(i) are i.i.d. with mean 0 and finite second moment and the ai are either summable or regularly varying with index epsilon (- 1, - 1/2). The sequence {X-n} has short memory in the former case and long memory in the latter. For a large class of functions K, a new approach is proposed to develop both central (root n rate) and noncentral (non-root n rate) limit theorems for S-N = Sigma(n=1)(N) [K(X-n) - EK(X-n)]. Specifically,...
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作者：Gine, E; Gotze, F; Mason, DM
作者单位：University of Connecticut; University of Connecticut; University of Bielefeld; University of Delaware
摘要：Let X, X-i, i is an element of N, be independent, identically distributed random variables. It is shown that the Student t-statistic based upon the sample {X-i}(i less than or equal to 1)(n) is asymptotically N(0, 1) if and only if X is in the domain of attraction of the normal law. It is also shown that, for any X, if the self-normalized sums U-n := Sigma(i=1)(n) X-i/(Sigma(i=1)(n) X-i(2))(1/2), n is an element of N, are stochastically bounded then they are uniformly subgaussian that is, sup(...
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作者：Leuridan, C
作者单位：Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
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作者：Voit, M
作者单位：Eberhard Karls University of Tubingen
摘要：In this paper we prove central limit theorems of the following kind: let S-d subset of Rd+1 be the unit sphere of dimension d greater than or equal to 2 with uniform distribution omega(d). For each k is an element of N, consider the isotropic random walk (X-n(k))(n greater than or equal to 0) on S-d starting at th north pole with jumps of fixed sizes angle(X-n(k), X-n-1(k)) = pi/root k for all n greater than or equal to 1. Then there is some k(0)(d) such that for all k greater than or equal to...
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作者：Darling, RWR; Pardoux, E
作者单位：State University System of Florida; University of South Florida; Aix-Marseille Universite
摘要：Suppose {T-t} is the filtration induced by a Wiener process W in R-d, tau is a finite {T-t} stopping time (terminal time), xi is an T-tau-measurable random variable in R-k (terminal value) and f(., y, z) is a coefficient process, depending on y is an element of R-k and z is an element of L(R-d; R-k), satisfying (y - (y) over bar) [f(s, y, z) - f(s, (y) over bar, z)] less than or equal to -a/y - (y) over bar/(2) (f need not be Lipschitz in Y), and /f(s, y, z) -f(s, y (z) over bar/ less than or ...
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作者：Dembo, A
作者单位：Stanford University; Stanford University
摘要：We derive inequalities of the form Delta(P, Q) less than or equal to H(P\R) + H(Q\R) which hold for every choice of probability measures P, Q, R, where H(P\R) denotes the relative entropy of P with respect to R acid Delta(P, Q) stands for a coupling type distance between P and Q. Using the chain rule for relative entropies and then specializing to Q with a given support we recover some of Talagrand's concentration of measure inequalities for product spaces.
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作者：de Fitte, PR
作者单位：Universite de Rouen Normandie
