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作者：MARCUS, MB; ROSEN, J
作者单位：Texas A&M University System; Texas A&M University College Station; City University of New York (CUNY) System; College of Staten Island (CUNY)
摘要：Let {L(t)x, (t, x) is-an-element-of R+ X T} be the local time of a real-valued symmetric stable process of order 1 < beta less-than-or-equal-to 2 and let {pi(n)} be a sequence of partitions of [0, a]. Results are obtained for [GRAPHICS] both almost surely and in L(r) for all r > 0. Results are also obtained for a similar expression but where the supremum of the sum is taken over all partitions of [0, a] and a function other than a power is applied to the increments of the local times. The proo...
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作者：SHEEHY, A; WELLNER, JA
作者单位：University of Washington; University of Washington Seattle
摘要：A class F of measurable functions on a probability space (A, A, P) is called a P-Donsker class and we also write F is-an-element-of CLT(P), if the empirical processes X(n)P = square-root n (P(n) - P) converge weakly to a P-Brownian bridge G(P) having bounded uniformly continuous sample paths almost surely. If this convergence holds for every probability measure P on (A, A), then F is called a universal Donsker class and we write F is-an-element-of CLT(M), where M = {all probability measures on...
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作者：KESTEN, H; MALLER, RA
作者单位：University of Western Australia
摘要：Let X(i) be independent and identically distributed random variables with distribution F. Let M(n)(n) less-than-or-equal-to ... less-than-or-equal-to M(n)(1) be the sample X1, X2,..., X(n) arranged in increasing order, with a convention for the breaking of ties, and let X(n)(n),..., X(n)(1) be the sample arranged in increasing order of modulus, again with a convention to break ties. Let S(n) = X1 + ... +X(n) be the sample sum. We consider sums trimmed by large values, (r)S(n) = S(n) - M(n)(1) ...
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作者：LALLEY, SP
摘要：It is proved that if a rational mapping has infinity as a fixed point in its Fatou set, then its Julia set has positive capacity and the equilibrium measure is invariant. If infinity is attracting or superattracting, then the equilibrium measure is strongly mixing, whereas if infinity is neutral, then the equilibrium measure is ergodic and has entropy zero. Lower bounds for the entropy are given in the attracting and superattracting cases. If the Julia set is totally disconnected, then the equ...
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作者：LYONS, R
作者单位：Stanford University
摘要：A collection of several different probabilistic processes involving trees is shown to have an unexpected unity. This makes possible a fruitful interplay of these probabilistic processes. The processes are allowed to have arbitrary parameters and the trees are allowed to be arbitrary as well. Our work has five specific aims: First, an exact correspondence between random walks and percolation on trees is proved, extending and sharpening previous work of the author. This is achieved by establishi...
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作者：MOUNTFORD, TS
摘要：We prove that the critical value for the uniform nearest particle system equals 1.
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作者：MARCUS, MB; ROSEN, J
作者单位：City University of New York (CUNY) System; College of Staten Island (CUNY); Texas A&M University System; Texas A&M University College Station; Technion Israel Institute of Technology
摘要：Necessary and sufficient conditions are obtained for the almost sure joint continuity of the local time of a strongly symmetric standard Markov process X. Necessary and sufficient conditions are also obtained for the almost sure global boundedness and unboundedness of the local time and for the almost sure continuity, boundedness and unboundedness of the local time in the neighborhood of a point in the state space. The conditions are given in terms of the 1-potential density of X. The proofs r...
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作者：PEMANTLE, R
作者单位：Cornell University
摘要：The contact process on an infinite homogeneous tree is shown to exhibit at least two phase transitions as the infection parameter lambda is varied. For small values of lambda a single infection eventually dies out. For larger lambda the infection lives forever with positive probability but eventually leaves any finite set. (The survival probability is a continuous function of lambda, and the proof of this is much easier than it is for the contact process on d-dimensional integer lattices.) For...
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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...
