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作者：Alexander, Kenneth S.
作者单位：University of Southern California
摘要：We prove a central limit theorem for the length of the minimal spanning tree of the set of sites of a Poisson process of intensity lambda in [0, 1](2) as lambda -> infinity. As observed previously by Ramey, the main difficulty is the dependency between the contributions to this length from different regions of [0, 1](2); a percolation-theoretic result on circuits surrounding a fixed site can be used to control this dependency. We prove such a result via a continuum percolation version of the R...
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作者：Fishman, George S.
作者单位：University of North Carolina; University of North Carolina Chapel Hill
摘要：This paper studies several different plans for selecting coordinates for updating via Gibbs sampling. It exploits the inherent features of the Gibbs sampling formulation, most notably its neighborhood structure, to characterize and compare the plans with regard to convergence to equilibrium and variance of the sample mean. Some of the plans rely completely or almost completely on random coordinate selection. Others use completely or almost completely deterministic coordinate selection rules. W...
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作者：Silvestrov, Dmitrii S.
作者单位：Umea University
摘要：Recurrence relations and upper bounds are obtained for power moments of generalized hitting times for semi-Markov processes. General necessary and sufficient conditions for the existence of these moments are also found. Applications to hitting times for semi-Markov dynamical systems of linear type, semi-Markov random walks, diffusion processes and queuing systems are discussed.
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作者：Karatzas, I.; Kou, S. G.
作者单位：Columbia University; Rutgers University System; Rutgers University New Brunswick
摘要：We discuss the problem of pricing contingent claims, such as European call options, based on the fundamental principle of absence of arbitrage and in the presence of constraints on portfolio choice, for example, incomplete markets and markets with short-selling constraints. Under such constraints, we show that there exists an arbitrage-free interval which contains the celebrated Black-Scholes price (corresponding to the unconstrained case); no price in the interior of this interval permits arb...
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作者：Brown, Timothy C.; Greig, Darryl
作者单位：University of Melbourne
摘要：Monotonicity properties of certain classes of point processes with respect to the Palm measure are exploited to derive upper and lower bounds on the total variation distance away from Poisson of these processes. The results obtained are applied to new better than used and new worse than used renewal processes and to a Cox process with rates given by a two state Markov chain.
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作者：Ji, Chuanshu; Seymour, Lynne
作者单位：University of North Carolina; University of North Carolina Chapel Hill; University System of Georgia; University of Georgia
摘要：Motivated by applications in texture synthesis, we propose a model selection procedure for Markov random fields based on penalized pseudo-likelihood. The procedure is shown to be consistent for choosing the true model, even for Gibbs random fields with phase transitions. As a by-product, rates for the restricted mean-square error and moderate deviation probabilities are derived for the maximum pseudolikelihood estimator. Some simulation results are presented for the selection procedure.
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作者：Penrose, Mathew D.
作者单位：Durham University
摘要：We prove that for continuum percolation in R-d, parametrized by the mean number y of points connected to the origin, as d -> infinity with y fixed the distribution of the number of points in the cluster at the origin converges to that of the total number of progeny of a branching process with a Poisson(y) offspring distribution. We also prove that for sufficiently large d the critical points for the existence of infinite occupied and vacant regions are distinct. Our results resolve conjectures...
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作者：Kirschenhofer, Peter; Prodinger, Helmut
作者单位：Technische Universitat Wien
摘要：In this tutorial, statistics on the number of people who tie for first place are considered. It is demonstrated that the so-called Rice's method from the calculus of finite differences is a very convenient tool both to rederive known results as well as to gain new ones with ease.
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作者：Rhee, Wansoo T.; Talagrand, Michel
作者单位：University System of Ohio; Ohio State University; University System of Ohio; Ohio State University; Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS)
摘要：A packing of a collection of subintervals of [0,1] is a pairwise disjoint subcollection of the intervals; its wasted space is the measure of the set of points not covered by the packing. Consider n random intervals, I-1,...,I-n , chosen by selecting endpoints independently from the uniform distribution. We strengthen and simplify the results of Coffman, Poonen and Winkler, and we show that, for some universal constant K and for each t >= 1, with probability greater than or equal to 1 - 1/n(t),...
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作者：Ferrari, P. A.; Kesten, H.; Martinez, S.
作者单位：Universidade de Sao Paulo; Cornell University; Universidad de Chile
摘要：We prove that certain (discrete time) probabilistic automata which can be absorbed in a null state have a normalized quasi-stationary distribution (when restricted to the states other than the null state). We also show that the conditional distribution of these systems, given that they are not absorbed before time n, converges to an honest probability distribution; this limit distribution is concentrated on the configurations with only finitely many active or occupied sites. A simple example t...
