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作者：Yao, Yi-Ching
作者单位：Academia Sinica - Taiwan; Colorado State University System; Colorado State University Fort Collins
摘要：For an infinite sequence of independent and identically distributed (i.i.d.) random variables, the k-record process consists of those terms that are the kth largest at their appearance. Ignatov's theorem states that the k-record processes, k = 1, 2,..., are i.i.d. A new proof is given which is based on a continualization'' argument. An advantage of this fairly simple approach is that Ignatov's theorem can be stated in a more general form by allowing for different tiebreaking rules. In particul...
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作者：Comets, Francis
作者单位：University of California System; University of California Irvine
摘要：We propose a new empirical procedure for detecting phase transition from a single sample of a Gibbs-Markov random field. The method is based on frequencies for large deviations when the whole sample is divided in smaller blocks and estimates for the rate function. We relate our approach to an almost sure large deviation principle.
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作者：Niu, Xu-Feng
作者单位：State University System of Florida; Florida State University; State University System of Florida; Florida State University
摘要：Consider a class of nonstationary time series with the form Y-t = mu t + xi(t) where {xi(t)} is a sequence of infinite moving averages of independent random variables with regularly varying tail probabilities and different scale parameters. In this article, the extreme value theory of {Y-t} is studied. Under mild conditions, convergence results for a point process based on the moving averages are proved, and extremal properties of the nonstationary time series, including the convergence of max...
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作者：Rucinski, A.; Wormald, N. C.
作者单位：Adam Mickiewicz University; University of Melbourne
摘要：Suppose that a process begins with n isolated vertices, to which edges are added randomly one by one so that the maximum degree of the induced graph is always at most 2. In a previous article, the authors showed that as n -> infinity, with probability tending to 1, the result of this process is a graph with n edges. The number of l-cycles in this graph is shown to be asymptotically Poisson (l >= 3), and other aspects of this random graph model are studied.
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作者：Kleptsina, M. L.; Liptser, R. Sh; Serebrovski, A. P.
作者单位：Russian University of Transport; Tel Aviv University
摘要：We give an approximation for optimal filtering estimates of a diffusion type signal and its observation under contamination affecting their drifts. The method of analysis is based on the averaging principle and convergence in total variation for distributions of signal and observation.
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作者：Denardo, Eric V.; Feinberg, Eugene A.; Kella, Offer
作者单位：Yale University; State University of New York (SUNY) System; Stony Brook University; Hebrew University of Jerusalem
摘要：This paper deals with first passage heights of sums of renewal sequences, random walks, and Levy processes. We prove that the joint age and excess (and therefore, the current life. stationary distributions of these heights are stochastically increasing (in the usual first-order sense. in the passage levels. As a preliminary tool, which is also of independent interest, a new decomposition of the stationary excess distribution, as a convolution of two other distributions, is developed. As a cons...
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作者：Lee, Sungchul
作者单位：National University of Singapore
摘要：Let {X-i : i >= 1} be i.i.d. with uniform distribution [-1/2, 1/2](d), d >= 2, and let T-n be a minimal spanning tree on {X-1,..., X-n}. For each strictly positive integer alpha, let N({X-1,..., X-n}; alpha) be the number of vertices of degree alpha in T-n. Then, for each alpha such that P(N({X-1,..., X alpha+1}; alpha) = 1. > 0, we prove a central limit theorem for N({X-1,..., X-n}; alpha).
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作者：Durrett, Rick; Neuhauser, Claudia
作者单位：Cornell University; University of Minnesota System; University of Minnesota Twin Cities; University of Wisconsin System; University of Wisconsin Madison
摘要：Barley yellow dwarf is a widespread disease that affects small grains and many grass species, as well as wheat, barley and oat. The disease is caused by an aphid transmitted virus. Rochow conducted a study near Ithaca, New York, which showed that a shift in the dominant strain occurred between 1957 and 1976. Motivated by this phenomenon, we develop a model for the competition between different strains of the barley yellow dwarf virus. Our main goal is to understand the phase diagram of the mod...
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作者：Heath, David; Resnick, Sidney; Samorodnitsky, Gennady
作者单位：Cornell University
摘要：We study the time it takes until a fluid queue with a finite, but large, holding capacity reaches the overflow point. The queue is fed by an on/off process with a heavy tailed on distribution which is known to have long memory. It turns out that the expected time until overflow, as a function of capacity L, increases only polynomially fast; so overflows happen much more often than in the classical light tailed case, where the expected overflow time increases as an exponential function of L. Mo...
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作者：Ball, Frank; Mollison, Denis; Scalia-Tomba, Gianpaolo
作者单位：University of Nottingham; Heriot Watt University; Sapienza University Rome
摘要：We consider epidemics with removal (SIR epidemics) in populations that mix at two levels: global and local. We develop a general modelling framework for such processes, which allows us to analyze the conditions under which a large outbreak is possible, the size of such outbreaks when they can occur and the implications for vaccination strategies, in each case comparing our results with the simpler homogeneous mixing case. More precisely, we consider models in which each infectious individual i...
