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作者：EVANS, SN
摘要：We consider a class of stochastic processes of a type that was first introduced by Dubins and Freedman. These processes are indexed by the lines of descent through an infinite tree and take values in a space of sequences. Our main results concern necessary and sufficient conditions of a potential theoretic type for a subset of the state-space to be hit with positive probability by the sample paths of the process. We examine these conditions in some specific examples and also relate them to con...
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作者：CHEN, HN
摘要：In this paper we study a growth model known as the contact process with sexual reproduction on Z2. We focus on the symmetric model in which a child particle can be produced at a vacant site whenever a pair of its neighboring sites is occupied by parent particles. Two kinds of stability of the absorbing state-phi (i,e., the state in which all the sites are vacant) are investigated in this paper. The first kind of stability concerns the behavior of the system when it starts close to the state-ph...
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作者：HENZE, N; VOIGT, B
摘要：Let X(j)(i), i = 1,..., k; j is-an-element-of N, be independent d-dimensional random vectors which are identically distributed for each fixed i = 1,..., k. We give a sufficient condition for almost sure convergence of a sequence T(n1,...,n(k)) of statistics based on X(j)(i) i = 1,....k; j = 1,...,n(i), which are symmetric functions of X1(i),...,X(n(i))(i) for each i and do not change too much when variables are added or deleted. A key auxiliary tool for proofs is the Efron-Stein inequality. Ap...
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作者：FITZSIMMONS, PJ; KANDA, M
作者单位：University of Tsukuba
摘要：Following Choquet, the capacity associated with a Markov process is said to be dichotomous if each compact set K contains two disjoint sets with the same capacity as K. In the context of right processes, we prove that the dichotomy of capacity is equivalent to Hunt's hypothesis that semipolar sets are polar. We also show that a weaker form of the dichotomy is valid for any Levy process with absolutely continuous potential kernel.
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作者：HAHN, MG; WEINER, DC
作者单位：Boston University
摘要：Let {X(j)} be independent, identically distributed random variables with continuous nondegenerate distribution F which is symmetric about the origin. Let {X(n)(1), X(n)(2), . . . , X(n)(n)} denote the arrangement of {X1, . . ., X(n)} in decreasing order of magnitude, so that with probability 1, \X(n)(1)\ > \X(n)(2)\ > ... > \X(n)(n)\. For integers r(n) --> infinity such that r(n)/n --> 0, define the self-normalized trimmed sum T(n) = SIGMA(i = r(n))nX(n)(i)/{SIGMA(i = r(n))nX(n)2(i)}1/2. The a...
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作者：BOUGEROL, P; PICARD, N
作者单位：Universite de Lorraine
摘要：In this paper we consider the multivariate equation X(n+1) = A(n+1)X(n) + B(n+1) with i.i.d. coefficients which have only a logarithmic moment. We give a necessary and sufficient condition for existence of a strictly stationary solution independent of the future. As an application we characterize the multivariate ARMA equations with general noise which have such a solution.
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作者：DELAPENA, VH
摘要：In this paper we introduce a fairly general decoupling inequality for U-statistics. Let {X(i)} be a sequence of independent random variables in a measurable space (S, F), and let (X(i)} be an independent copy of {X(i)}. Let PHI(x) be any convex increasing function for x greater-than-or-equal-to 0. Let PI(ij) be families of functions of two variables taking (S x S) into a Banach space (D, parallel-to . parallel-to). If the f(ij) is-an-element-of PI(ij) are Bochner integrable and [GRAPHICS] then...
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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...
