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作者：Larsen, Kasper; Zitkovic, Gordan
作者单位：Carnegie Mellon University; University of Texas System; University of Texas Austin
摘要：We consider a utility-maximization problem in a general semimartingale financial model, subject to constraints on the number of shares held in each risky asset. These constraints are modeled by predictable convex-set-valued processes whose values do not necessarily contain the origin; that is, it may be inadmissible for an investor to hold no risky investment at all. Such a setup subsumes the classical constrained utility-maximization problem, as well as the problem where illiquid assets or a ...
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作者：Giesecke, Kay; Spiliopoulos, Konstantinos; Sowers, Richard B.
作者单位：Stanford University; Brown University; University of Illinois System; University of Illinois Urbana-Champaign
摘要：We develop a dynamic point process model of correlated default timing in a portfolio of firms, and analyze typical default profiles in the limit as the size of the pool grows. In our model, a firm defaults at a stochastic intensity that is influenced by an idiosyncratic risk process, a systematic risk process common to all firms, and past defaults. We prove a law of large numbers for the default rate in the pool, which describes the typical behavior of defaults.
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作者：Khare, Kshitij; Mukherjee, Nabanita
作者单位：State University System of Florida; University of Florida; University of Pennsylvania; Pennsylvania Medicine; Childrens Hospital of Philadelphia
摘要：We provide a nonasymptotic analysis of convergence to stationarity for a collection of Markov chains on multivariate state spaces, from arbitrary starting points, thereby generalizing results in [Khare and Zhou Ann. Appl. Probab. 19 (2009) 737-777]. Our examples include the multi-allele Moran model in population genetics and its variants in community ecology, a generalized Ehrenfest urn model and variants of the Polya urn model. It is shown that all these Markov chains are stochastically monot...
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作者：Lambert, Amaury; Simatos, Florian; Zwart, Bert
作者单位：Sorbonne Universite; Centrum Wiskunde & Informatica (CWI); Vrije Universiteit Amsterdam
摘要：We study the convergence of the M/G/1 processor-sharing, queue length process in the heavy traffic regime, in the finite variance case. To do so, we combine results pertaining to Levy processes, branching processes and queuing theory. These results yield the convergence of long excursions of the queue length processes, toward excursions obtained from those of some reflected Brownian motion with drift, after taking the image of their local time process by the Lamperti transformation. We also sh...
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作者：Radin, Charles; Yin, Mei
作者单位：University of Texas System; University of Texas Austin
摘要：We derive the full phase diagram for a large family of two-parameter exponential random graph models, each containing a first order transition curve ending in a critical point.
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作者：Bramson, Maury; Lu, Yi; Prabhakar, Balaji
作者单位：University of Minnesota System; University of Minnesota Twin Cities; University of Illinois System; University of Illinois Urbana-Champaign; Stanford University
摘要：In join the shortest queue networks, incoming jobs are assigned to the shortest queue from among a randomly chosen subset of D queues, in a system of N queues; after completion of service at its queue, a job leaves the network. We also assume that jobs arrive into the system according to a rate-alpha N Poisson process, alpha < 1, with rate-1 service at each queue. When the service at queues is exponentially distributed, it was shown in Vvedenskaya et al. [Probl. Inf. Transm. 32 (1996) 15-29] t...
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作者：Leao, Dorival; Ohashi, Alberto
作者单位：Universidade de Sao Paulo; Universidade Federal da Paraiba
摘要：In this paper we introduce a simple space-filtration discretization scheme on Wiener space which allows us to study weak decompositions and smooth explicit approximations for a large class of Wiener functionals. We show that any Wiener functional has an underlying robust semimartingale skeleton which under mild conditions converges to it. The discretization is given in terms of discrete-jumping filtrations which allow us to approximate nonsmooth processes by means of a stochastic derivative op...
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作者：Fill, James Allen
作者单位：Johns Hopkins University
摘要：Most previous studies of the sorting algorithm QuickSort have used the number of key comparisons as a measure of the cost of executing the algorithm. Here we suppose that the n independent and identically distributed (i.i.d.) keys are each represented as a sequence of symbols from a probabilistic source and that QuickSort operates on individual symbols, and we measure the execution cost as the number of symbol comparisons. Assuming only a mild tameness condition on the source, we show that the...
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作者：Laruelle, Sophie; Pages, Gilles
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite; Universite Paris Cite
摘要：This paper presents the link between stochastic approximation and clinical trials based on randomized urn models investigated by Bai and Hu [Stochastic Process. Appl. 80 (1999) 87-101], Bai and Hu [Ann. Appl. Probab. 15 (2005) 914-940] and Bai, Hu and Shen [J. Multivariate Anal. 81 (2002) 1-18]. We reformulate the dynamics of both the urn composition and the assigned treatments as standard stochastic approximation (SA) algorithms with remainder. Then, we derive the as. convergence and the asym...
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作者：Durrett, Rick
作者单位：Duke University
摘要：In order to analyze data from cancer genome sequencing projects, we need to be able to distinguish causative, or driver, mutations from passenger mutations that have no selective effect. Toward this end, we prove results concerning the frequency of neutural mutations in exponentially growing multitype branching processes that have been widely used in cancer modeling. Our results yield a simple new population genetics result for the site frequency spectrum of a sample from an exponentially grow...
