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作者：Dennert, Florian; Gruebel, Rudolf
作者单位：Leibniz University Hannover
摘要：We show that the number of renewals up to time t exhibits distributional fluctuations as t -> infinity if the underlying lifetimes increase at an exponential rate in a distributional sense. This provides a probabilistic explanation for the asymptotics of insertion depth in random trees generated by a bit-comparison strategy from uniform input; we also obtain a representation for the resulting family of limit laws along subsequences. Our approach can also be used to obtain rates of convergence.
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作者：Janssen, A. J. E. M.; van Leeuwaarden, J. S. H.
作者单位：Philips; Philips Research
摘要：Let X-1, X-2.... be independent variables, each having a normal distribution with negative mean -beta < 0 and variance 1. We consider the partial sums Sn = X-1 + - - - + X-n, with S-0 = 0, and refer to the process {S-n : n >= 0} as the Gaussian random walk. We present explicit expressions for the mean and variance of the maximum M = max{S-n : n > 0}. These expressions are in terms of Taylor series about beta = 0 with coefficients that involve the Riemann zeta function. Our results extend Kingm...
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作者：Heffernan, Janet E.; Resnick, Sidney I.
作者单位：Lancaster University; Cornell University
摘要：Models based on assumptions of multivariate regular variation and hidden regular variation provide ways to describe a broad range of extremal dependence structures when marginal distributions are heavy tailed. Multivariate regular variation provides a rich description of extremal dependence in the case of asymptotic dependence, but fails to distinguish between exact independence and asymptotic independence. Hidden regular variation addresses this problem by requiring components of the random v...
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作者：Hutzenthaler, M.; Wakolbinger, A.
作者单位：Goethe University Frankfurt
摘要：For a class of processes modeling the evolution of a spatially structured population with migration and a logistic local regulation of the reproduction dynamics, we show convergence to an upper invariant measure from a suitable class of initial distributions. It follows from recent work of Alison Etheridge that this upper invariant measure is nontrivial for sufficiently large super-criticality in the reproduction. For sufficiently small super-criticality, we prove local extinction by compariso...
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作者：Bally, Vlad; Bavouzet, Marie-Pierre; Messaoud, Marouen
作者单位：Universite Gustave-Eiffel; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris-Est-Creteil-Val-de-Marne (UPEC)
摘要：We consider random variables of the form F = f(V-1,..., V-n), where f is a smooth function and Vi, i EN, are random variables with absolutely continuous law p(i) (y) dy. We assume that p(i), i = 1,..., n, are piecewise differentiable and we develop a differential calculus of Malliavin type based on a In pi. This allows us to establish an integration by parts formula E(delta i phi(F)G) = E(phi(F)H-i(F, G)), where H-i(F, G) is a random variable constructed using the differential operators acting...
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作者：Russo, Ralph P.; Shyamalkumar, Nariankadu D.
作者单位：University of Iowa
摘要：Suppose that mn observations are made from the distribution R and n - m(n) from the distribution S. Associate with each pair, x from R and y from S, a nonnegative score phi(x, y). An optimal reading policy is one that yields a sequence mn that maximizes E(M(n)), the expected sum of the (n - mn)mn observed scores, uniformly in n. The alternating policy, which switches between the two sources, is the optimal nonadaptive policy. In contrast, the greedy policy, which chooses its source to maximize...
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作者：Gromoll, Christian; Kruk, Lukasz
作者单位：Stanford University; Maria Curie-Sklodowska University
摘要：This paper considers a GI/GI/1 processor sharing queue in which jobs have soft deadlines. At each point in time, the collection of residual service times and deadlines is modeled using a random counting measure on the right half-plane. The limit of this measure valued process is obtained under diffusion scaling and heavy traffic conditions and is characterized as a deterministic function of the limiting queue length process. As special cases, one obtains diffusion approximations for the lead t...
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作者：Chi, Zhiyi
作者单位：University of Connecticut
摘要：Let (X-n, Y-n) be i.i.d. random vectors. Let W(x) be the partial sum of Yn just before that of X-n exceeds x > 0. Motivated by stochastic models for neural activity, uniform convergence of the form sup(c is an element of I) vertical bar a(c, x) Pr{W(x) >= cx} - 1 vertical bar = o(1), x -> infinity, is established for probabilities of large deviations, with a (c, x) a deterministic function and I an open interval. To obtain this uniform exact large deviations principle (LDP), we first establish...
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作者：Git, Y.; Harris, J. W.; Harris, S. C.
作者单位：University of Cambridge; University of Bristol; University of Bath
摘要：We study the high temperature phase of a family of typed branching diffusions initially studied in [Asterisque 236 (1996) 133-154] and [Lecture Notes in Math. 1729 (2000) 239-256 Springer, Berlin]. The primary aim is to establish some almost-sure limit results for the long-term behavior of this particle system, namely the speed at which the population of particles colonizes both space and type dimensions, as well as the rate at which the population grows within this asymptotic shape. Our appro...
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作者：Krieger, Abba M.; Pollak, Moshe; Samuel-Cahn, Ester
作者单位：University of Pennsylvania; Hebrew University of Jerusalem
摘要：In many situations, the decision maker observes items in sequence and needs to determine whether or not to retain a particular item immediately after it is observed. Any decision rule creates a set of items that are selected. We consider situations where the available information is the rank of a present observation relative to its predecessors. Certain natural selection rules are investigated. Theoretical results are presented pertaining to the evolution of the number of items selected, measu...
