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作者：Stacey, AM
摘要：Let T-d be a homogeneous tree in which every vertex has d neighbors. A new proof is given that the contact process on T-d exhibits two phase transitions when d greater than or equal to 3, a behavior which distinguishes it from the contact process on Z(n). This is the first proof which does not involve calculation of bounds on critical values, and it is much shorter than the previous proof for the binary tree, T-3. The method is extended to prove the existence of an intermediate phase for a mor...
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作者：Pritchard, G
摘要：The scaled-sample problem asks the following question: given a distribution on a normed linear space E, when do there exist constants {gamma(n)} such that {X((j))/gamma(n)}(n)(j=1) converges as n --> infinity (in the Hausdorff metric given by the norm) to a fixed set K? (Here {X((j))} i.i.d. with the given distribution.) The main result presented here relates the convergence of scaled samples to a large deviation principle for single observations, thereby achieving a dimension-free description...
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作者：Glynn, PW; Meyn, SP
作者单位：University of Illinois System; University of Illinois Urbana-Champaign
摘要：In this paper we consider psi-irreducible Markov processes evolving in discrete or continuous time on a general state space. We develop a Liapounov function criterion that permits one to obtain explicit bounds on the solution to the Poisson equation and, in particular, obtain conditions under which the solution is square integrable. These results are applied to obtain sufficient conditions that guarantee the validity of a functional central limit theorem for the Markov process. As a second con...
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作者：Houdre, C; Lacey, MT
作者单位：Indiana University System; Indiana University Bloomington
摘要：It is shown here how to extend the spectral characterization of the strong law of large numbers for weakly stationary processes to certain singular averages. For instance, letting {X(t), t is an element of R(3)} be a weakly stationary field, {X(t)} satisfies the usual SLLN (by averaging over balls) if and only if the averages of {X(t)} over spheres of increasing radii converge pointwise. The same result in two dimensions is false. This spectral approach also provides a necessary and sufficient...
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作者：Bentkus, V; Gotze, F
摘要：We prove optimal convergence rates in the central limit theorem for sums in R(k). Assuming a fourth moment, we obtain a Berry-Esseen type bound of O(N-1) for the probability of hitting a ball provided that k greater than or equal to 5. The proof still requires a technical assumption related to the independence of coordinates of sums.
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作者：Einmahl, JHJ
摘要：A short proof of the lower bound in the strong version of the famous Theorem IA in Kiefer (1970) on the Bahadur-Kiefer process is presented. The proof is elementary and, in particular, does not use strong approximations.
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作者：Bremaud, P; Massoulie, L
摘要：We address the problem of the convergence to equilibrium of a general class of point processes, containing, in particular, the nonlinear mutually exciting point processes, an extension of the linear Hawkes processes, and give general conditions guaranteeing the existence of a stationary version and the convergence to equilibrium of a nonstationary version, both in distribution and in variation. We also give a new proof of a result of Kerstan concerning point processes with bounded intensity an...
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作者：Klenke, A
摘要：We study a system of interacting diffusions dx xi(t) = Sigma(zeta is an element of Xi) a(xi,zeta)(x(zeta)(t) - x(xi)(t))dt + root g(x xi(t)) dW xi(t) (xi is an element of Xi), indexed by the hierarchical group Xi, as a genealogical two genotype model [where x(xi)(t) denotes the frequency of, say, type A] with hierarchically determined degrees of relationship between colonies. In the case of short interaction range it is known that the system clusters. That is, locally one genotype dies out. We...
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作者：Pruitt, WE; Taylor, SJ
作者单位：University of Virginia
摘要：There has been substantial interest in the indices 0 less than or equal to beta '' less than or equal to beta' less than or equal to beta less than or equal to 2 defined by Blumenthal and Getoor, determined by a general Levy process in R(d). Pruitt defined an index gamma which determines the covering dimension and Taylor showed that an index gamma', first considered by Hendricks, determines the packing dimension for the trajectory. In the present paper we prove that beta/2 less than or equal t...
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作者：Burdzy, K; Werner, W
作者单位：University of Cambridge; Centre National de la Recherche Scientifique (CNRS)
摘要：We show that the boundary of a connected component of the complement of a planar Brownian path on a fixed time interval contains almost surely no triple point of this Brownian path.
