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作者：Penrose, MD
作者单位：Durham University
摘要：Given an ordering of the vertices of a finite graph, let the induced weight for an edge be the separation of its endpoints in the ordering. Layout problems involve choosing the ordering to minimize a cost functional such as the sum or maximum of the edge weights. We give growth rates for the costs of some of these problems on supercritical percolation processes and supercritical random geometric graphs, obtained by placing vertices randomly in the unit cube and joining them whenever at most so...
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作者：Yin, G; Zhang, Q; Badowski, G
作者单位：Wayne State University; University System of Georgia; University of Georgia
摘要：This work is concerned with aggregations in a singularly perturbed Markov chain having a finite state space and fast and slow motions. The state space of the underlying Markov chain can be decomposed into several groups of recurrent states and a group of transient states. The asymptotic properties are studied through sequences of unscaled and scaled occupation measures. By treating the states within each recurrent class as a single state, an aggregated process is defined and shown to be conver...
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作者：Bouchard, B; Touzi, N
作者单位：Universite PSL; Universite Paris-Dauphine
摘要：We consider a multivariate financial market with transaction costs as in Kabanov. We study the problem of finding the minimal initial capital needed to hedge, without risk, European-type contingent claims. We prove that the value of this stochastic control problem is given by the cost of the cheapest buy-and-hold strategy. This is an extension of the already known result in the one-dimensional case. An important feature of our analysis is that we do not make use of the dual formulation of the ...
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作者：Giraitis, L; Robinson, PM; Surgailis, D
作者单位：University of London; London School Economics & Political Science; Vilnius University
摘要：For a particular conditionally heteroscedastic nonlinear (ARCH) process for which the conditional variance of the observable sequence r(t) is the square of an inhomogeneous linear combination of r(s), s < t, we give conditions under which, for integers l 2, r(t)(l) has long memory autocorrelation and normalized partial sums of r(t)(l) converge to fractional Brownian motion.
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作者：Ignatiouk-Robert, I
作者单位：CY Cergy Paris Universite
摘要：The problem of large deviations for a Jackson network is analyzed in detail. A new representation of the rate function is given and a simple procedure is proposed to get its closed form expression. The methods used rely on twisted distributions, localized processes, fluid limits and II careful analysis of some functions.
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作者：Karlin, S; Chen, CF
作者单位：Stanford University
摘要：This study is motivated by problems of molecular sequence comparisons for biological traits conserved or lost over evolution time. A marker of interest is distributed in the genome of the ancestor and inherited among I offspring species which descend from this common ancestor. Each marker will be retained or lost during the evolution of the descendent species. The objective of the analysis here is to ascertain probabilities of clustering or overdispersion of the marker array among the sequence...
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作者：O'Cinneide, CA; Pokrovskii, AV
作者单位：Purdue University System; Purdue University; University College Cork
摘要：With a given transformation on a finite domain, we associate a three-dimensional distribution function describing the component size, cycle length and trajectory length of each point in the domain. We then consider a random transformation on the domain, in which images of points are independent and identically distributed. The three-dimensional distribution function associated with this random transformation is itself random. We show that, under a simple homogeneity condition on the distributi...
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作者：Erhardsson, T
作者单位：Royal Institute of Technology
摘要：We consider the number of overlapping occurrences up to a fixed time of one or several rare patterns in a stationary finite-state Markov chain. We derive a bound for the total variation distance between the distribution of this quantity and a compound Poisson distribution, using general results on compound Poisson approximation for Markov chains by Erhardsson. If the state space is {0, 1} and the pattern is a head run (111...111), the bound is completely explicit and improves on an earlier bou...
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作者：Barbour, AD; Ethier, SN; Griffiths, RC
作者单位：University of Zurich; Utah System of Higher Education; University of Utah; Monash University
摘要：Using duality, an expansion is found for the transition function of the reversible K-allele diffusion model in population genetics. In the neutral case, the expansion is explicit but already known. When selection is present, it depends on the distribution at time t of a specified R-type birth-and-death process starting at infinity. The latter process is constructed by means of a coupling argument and characterized as the Ray process corresponding to the Ray-Knight compactification of the K-dim...
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作者：Fannjiang, A; Komorowski, T
作者单位：University of California System; University of California Davis; Maria Curie-Sklodowska University; Polish Academy of Sciences
摘要：We show that the motion of a particle advected by a random Gaussian velocity held with long-range correlations converges to a fractional Brownian motion in the long time limit.
