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作者：Evans, SN; Sowers, RB
作者单位：University of California System; University of California Berkeley; University of Illinois System; University of Illinois Urbana-Champaign
摘要：We develop a technique for partially collapsing one Markov process to produce another. The state space of the new Markov process is obtained by a pinching operation that identifies points of the original state space via an equivalence relationship. To ensure that the new process is Markovian we need to introduce a randomized twist according to an appropriate probability kernel. Informally, this twist randomizes over the uncollapsed. region of the state space when the process leaves the collaps...
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作者：Mairesse, J; Prabhakar, B
作者单位：Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); Stanford University; Stanford University
摘要：A celebrated theorem of Burke's asserts that the Poisson process is a fixed point for a stable exponential single server queue; that is, when the arrival process is Poisson, the equilibrium departure process is Poisson of the same rate. This paper considers the following question: Do fixed points exist for queues which dispense i.i.d. services of finite mean, but otherwise of arbitrary distribution (i.e., the so-called (.)/GI/1/infinity/FCFS queues)? We show that if the service time S is nonco...
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作者：Chen, X; Li, WBV
作者单位：University of Tennessee System; University of Tennessee Knoxville; University of Delaware
摘要：Let the Gaussian process X-m(t) be the m-fold integrated Brownian motion for positive integer m. The Laplace transform of the quadratic functional of Xm(t) is found by using an appropriate self-adjoint integral operator. The result is then used to show the power of a general connection between small ball probabilities for the Gaussian process. The connection is discovered by introducing an independent random shift. The interplay between our results and the principal eigenvalues for nonuniform ...
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作者：Járai, AA
作者单位：University of British Columbia
摘要：We study several kinds of large critical percolation clusters in two dimensions. We show that from the microscopic (lattice scale) perspective these clusters can be described by Kesten's incipient infinite cluster (IIC), as was conjectured by Aizenman. More specifically, we establish this for incipient spanning clusters, large clusters in a finite box and the inhomogeneous model of Chayes, Chayes and Durrett. Our results prove the equivalence of several natural definitions of the IIC. We also ...
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作者：Lyons, R; Permantle, R
作者单位：Indiana University System; Indiana University Bloomington; University System of Georgia; Georgia Institute of Technology; University System of Ohio; Ohio State University
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作者：Jacka, S; Tribe, R
作者单位：University of Warwick
摘要：This paper considers some measure-valued processes {X-t:t is an element of [0, T]} based on an underlying critical branching particle structure with random branching rates. In the case of constant branching these processes are Dawson-Watanabe processes. Sufficient conditions on functionals Phi of the process are given that imply that the expectations E(Phi(X-T)) are comparable to the constant branching case. Applications to hitting estimates and regularity of solutions are discussed. The resul...
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作者：Harrelson, D; Houdré, C
作者单位：Hope College; Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); University System of Georgia; Georgia Institute of Technology
摘要：m-dependent stationary infinitely divisible sequences are characterized as a class of generalized finite moving average sequences via the structure of the associated Levy measure. This characterization is used to find necessary and sufficient conditions for the weak convergence of centered and normalized partial sums of m-dependent stationary infinitely divisible sequences. Partial sum convergence for stationary infinitely divisible sequences that can be approximated by m-dependent ones is the...
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作者：Prabhakar, B
作者单位：Stanford University; Stanford University
摘要：We consider an infinite tandem of first-come-first-served queues. The service times have unit mean, and are independent and identically distributed across queues and customers. Let I be a stationary and ergodic interarrival sequence with marginals of mean tau > 1, and suppose it is independent of all service times. The process I is said to be a fixed point for the first, and hence for each, queue if the corresponding interdeparture sequence is distributed as I. Assuming that such a fixed point...
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作者：Csörgö, M; Szyszkowicz, B; Wang, QY
作者单位：Carleton University; Australian National University
摘要：Let X, X-1, X-2,... be a sequence of nondegenerate i.i.d. random variables with zero means. In this paper we show that a self-normalized version of Donsker's theorem holds only under the assumption that X belongs to the domain of attraction of the normal law. A thus resulting extension of the arc sine law is also discussed. We also establish that a weak invariance principle holds true for self-normalized, self-randomized partial sums processes of independent random variables that are assumed t...
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作者：Marckert, JF; Mokkadem, A
作者单位：Universite Paris Saclay
摘要：In this paper, we show a strong relation between the depth first processes associated to Galton-Watson trees with finite variance, conditioned by the total progeny: the depth first walk, the depth first queue process, the height process; a consequence is that these processes (suitably normalized) converge to the same Brownian excursion. This provides an alternative proof of Aldous' one of the convergence of the depth first walk to the Brownian excursion which does not use the existence of a li...
