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作者：MASON, DM; SHORACK, GR
作者单位：University of Washington; University of Washington Seattle
摘要：It is now classical that the sample mean YBAR is known to be asymptotically normal with square-root n norming if and only if 0 < Var[Y] < infinity and with arbitrary norming if and only if the df of Y is in the domain of attraction of the normal df. Now let T(n) = n-1SIGMAc(ni)h(X(n:i)) for order statistics X(n:i) from a df F denote a general L-statistic subject to a bit of regularity; the key condition introduced into this problem in this paper is the regular variation of the score function J...
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作者：ARRATIA, R; TAVARE, S
摘要：The total variation distance between the process which counts cycles of size 1, 2,...,b of a random permutation of n objects and a process (Z1, Z2..... Z(b)) of independent Poisson random variables with EZ(i) = 1/i converges to 0 if and only if b/n --> 0. This Poisson approximation can be used to give simple proofs of limit theorems and bounds for a wide variety of functionals of random permutations. These limit theorems include the Erdos-Turin theorem for the asymptotic normality of the log o...
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作者：TALAGRAND, M
作者单位：Sorbonne Universite
摘要：For very general random Fourier series and infinitely divisible processes on a locally compact Abelian group G, a necessary and sufficient condition for sample continuity is given in terms of the convergence of a certain series. This series expresses a control on the covering numbers of a compact neighborhood of G by certain nonrandom sets naturally associated with the Fourier series (resp. the process). In the nonstationary case, we give a necessary Sudakov-type condition for a probability me...
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作者：DAY, MV
摘要：The small noise exit problem of Wentzell and Freidlin is of particular interest for regions whose boundary consists of trajectories of the underlying (unperturbed) dynamical system. This is called the case of characteristic boundary. One fruitful approach to attacking this problem involves conditioning the probability measure so that exit to the boundary occurs more quickly. In a previous paper, this approach was applied to some simplified examples, revealing some previously unanticipated phen...
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作者：DYNKIN, EB
摘要：We establish connections between superdiffusion processes and one class of nonlinear parabolic differential equations. Analytic results due to Brezis and Friedman, Baras and Pierre and others are used to investigate the graphs of superdiffusions. A survey of the literature and general comments are presented in Section 4.
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作者：KHOSHNEVISAN, D
作者单位：Massachusetts Institute of Technology (MIT)
摘要：We briefly show an extension of inequalities of Burkholder and Gundy for linear Brownian motion to certain monotone functionals of the d-dimensional Brownian convex hull. Our results belong to a class of results that imply that Brownian hulls are much like the one-dimensional maximal process.
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作者：LIGGETT, TM
摘要：Consider the inhomogeneous contact process on Z1 with recovery rate delta(k) at site k and infection rates lambda(k) and rho(k) at site k due to the presence of infected neighbors at k - 1 and k + 1 respectively. A special case of the main result in this paper is the following: Suppose that the environment is chosen in such a way that the delta(k)'s, lambda(k)'s and rho(k)'s are all mutually independent, with the delta(k)'s having a common distribution, and the lambda(k)'s and rho(k)'s having ...
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作者：BRYDGES, D; EVANS, SN; IMBRIE, JZ
作者单位：University of California System; University of California Berkeley; Harvard University; Harvard University
摘要：We define a Levy process on a d-dimensional hierarchical lattice. By construction the Green's function for this process decays as \x\2-d . For d = 4, we prove that the introduction of a sufficiently weak self-avoidance interaction does not change this decay provided the mass = killing rate is chosen in a special way, so that the process is critical.
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作者：FINNER, H
摘要：The main result of this article is a generalization of the generalized Holder inequality for functions or random variables defined on lower-dimensional subspaces of n-dimensional product spaces. It will be seen that various other inequalities are included in this approach. For example, it allows the calculation of upper bounds for the product measure of n-dimensional sets with the help of product measures of lower-dimensional marginal sets. Furthermore, it yields an interesting inequality for ...
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作者：FISCH, R
摘要：This paper investigates the dynamics of the one-dimensional three-color cyclic cellular automaton. The author has previously shown that this process fluctuates, meaning that each lattice site changes color infinitely often, so that there is no final state for the system. The focus of the current work is on the clustering properties of this system. This paper demonstrates that the one-dimensional three-color cyclic cellular automaton clusters, and the mean cluster size, as a function of time t,...
