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作者：Duffie, Darrell; Schroder, Mark; Skiadas, Costis
作者单位：Stanford University; State University of New York (SUNY) System; University at Buffalo, SUNY; Northwestern University
摘要：We derive the implications of default risk for valuation of securities in an abstract setting in which the fractional default recovery rate and the hazard rate for default may depend on the market value of the instrument itself, or on the market values of other instruments issued by the same entity (which are determined simultaneously). A key technique is the use of backward recursive stochastic integral equations. We characterize the dependence of the market value on the manner of resolution ...
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作者：Cohn, Harry
作者单位：University of Melbourne
摘要：Let {Zn} be a branching process whose offspring distributions vary with n. It is shown that the sequence {max(i > 0) P(Z(n) = i)} has a limit. Denote this limit by M. It turns out that M is positive only if the offspring variables rapidly approach constants. Let {c(n)} be a sequence of constants and Wn sZnrcn. It will be proven that M = 0 is necessary and sufficient for the limit distribution functions of all convergent {W-n} to be continuous on (0,infinity). If M > 0 there is, up to an equiva...
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作者：Gnedin, Alexander V.; Krengel, Ulrich
作者单位：University of Gottingen
摘要：We consider optimal stopping problems with loss function q depending on the rank of the stopped random variable. Samuels asked whether there exists an exchangeable sequence of random variables X-1,..., X-n without ties for which the observation of the values of the X-i's gives no advantage in comparison with the observation of just the relative ranks of the variables. We call distributions of the sequences with this property q-noninformative and derive necessary and sufficient conditions for t...
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作者：Yukich, J. E.
作者单位：Lehigh University
摘要：We show that the stochastic versions of some classical problems in combinatorial optimization may be imbedded in multiparameter subadditive processes having an intrinsic ergodic structure. A multiparameter generalization of Kingman's subadditive ergodic theorem is used to capture strong laws for these optimization problems, including the traveling salesman and minimal spanning tree processes. In this way we make progress on some open problems and provide alternate proofs of some well known asy...
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作者：Alsmeyer, Gerold; Roesler, Uwe
作者单位：University of Munster; University of Kiel
摘要：We consider the bisexual Galton-Watson process (BGWP) with promiscuous mating, that is, a branching process which behaves like an ordinary Galton-Watson process as long as at least one male is produced in each generation. For the case of Poissonian reproduction, it was pointed out by Daley, Hull and Taylor that the extinction probability of such a BGWP apparently behaves like a constant times the respective probability of its asexual counterpart (where males do not matter) providing the number...
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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：Barbour, A. D.; Heesterbeek, J. A. P.; Luchsinger, C. J.
作者单位：University of Zurich
摘要：We investigate the initial behavior of a deterministic model of parasitic infection, appropriate to transmission between homogeneously mixing hosts, where the amount of infection which is transferred from one host to another at a single contact depends on the number of parasites in the infecting host. In this model, R-0 can be defined to be the lifetime expected number of offspring of an adult parasite under ideal conditions, but it does not necessarily contain the information needed to separa...
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作者：Hwang, Hsien-Kuei
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; Academia Sinica - Taiwan
摘要：We prove a general central limit theorem for probabilities of large deviations for sequences of random variables satisfying certain analytic conditions. This theorem has wide applications to combinatorial structures and to the distribution of additive arithmetical functions. The method of proof is an extension of Kubilius' version of Cramer's classical method based on analytic moment generating functions. We thus generalize Cramer's and Kubilius's theorems on large deviations.
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作者：Lent, Janice; Mahmoud, Hosam M.
作者单位：George Washington University
摘要：Using the concept of a tree-growing'' search strategy, we prove that for most practical insertion sorting algorithms, the number of comparisons needed to sort n keys has asymptotically normal behavior. We prove and apply a sufficient condition for asymptotically normal behavior. The condition specifies a relationship between the variance of the number of comparisons and the rate of growth in height of the sequence of trees that the search strategy grows.''
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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...
