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作者：Harper, Adam J.
作者单位：University of Cambridge
摘要：We prove new lower bounds for the upper tail probabilities of suprema of Gaussian processes. Unlike many existing bounds, our results are not asymptotic, but supply strong information when one is only a little into the upper tail. We present an extended application to a Gaussian version of a random process studied by Halasz. This leads to much improved lower bound results for the sum of a random multiplicative function. We further illustrate our methods by improving lower bounds for some class...
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作者：Bouchard, Bruno; Taflin, Erik
作者单位：Institut Polytechnique de Paris; ENSAE Paris; Universite PSL; Universite Paris-Dauphine; CY Cergy Paris Universite; Ecole Internationale des Sciences du Traitement de linformation
摘要：Motivated by applications to bond markets, we propose a multivariate framework for discrete time financial markets with proportional transaction costs and a countable infinite number of tradable assets. We show that the no-arbitrage of second kind property (NA2 in short), recently introduced by Rasonyi for finite-dimensional markets, allows us to provide a closure property for the set of attainable claims in a very natural way, under a suitable efficient friction condition. We also extend to t...
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作者：Lindberg, Carl; Rootzen, Holger
作者单位：Chalmers University of Technology; University of Gothenburg
摘要：This paper proves joint convergence of the approximation error for several stochastic integrals with respect to local Brownian semimartingales, for nonequidistant and random grids. The conditions needed for convergence are that the Lebesgue integrals of the integrands tend uniformly to zero and that the squared variation and covariation processes converge. The paper also provides tools which simplify checking these conditions and which extend the range for the results. These results are used t...
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作者：Choi, Jihyeok; Sethuraman, Sunder
作者单位：Syracuse University; University of Arizona
摘要：Preferential attachment schemes, where the selection mechanism is linear and possibly time-dependent, are considered, and an infinite-dimensional large deviation principle for the sample path evolution of the empirical degree distribution is found by Dupuis-Ellis-type methods. Interestingly, the rate function, which can be evaluated, contains a term which accounts for the cost of assigning a fraction of the total degree to an infinite degree component, that is, when an atypical condensation ef...
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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：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：Loh, Po-Shen; Lubetzky, Eyal
作者单位：Carnegie Mellon University; Microsoft
摘要：The following distributed coalescence protocol was introduced by Dahlia Malkhi in 2006 motivated by applications in social networking. Initially there are n agents wishing to coalesce into one cluster via a decentralized stochastic process, where each round is as follows: every cluster flips a fair coin to dictate whether it is to issue or accept requests in this round. Issuing a request amounts to contacting a cluster randomly chosen proportionally to its size. A cluster accepting requests is...
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作者：Kang, Hye-Won; Kurtz, Thomas G.
作者单位：University of Minnesota System; University of Minnesota Twin Cities; University of Wisconsin System; University of Wisconsin Madison
摘要：A stochastic model for a chemical reaction network is embedded in a one-parameter family of models with species numbers and rate constants scaled by powers of the parameter. A systematic approach is developed for determining appropriate choices of the exponents that can be applied to large complex networks. When the scaling implies subnetworks have different time-scales, the subnetworks can be approximated separately, providing insight into the behavior of the full network through the analysis...
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作者：Czichowsky, Christoph; Schweizer, Martin
作者单位：University of Vienna; Swiss Federal Institutes of Technology Domain; ETH Zurich; Swiss Finance Institute (SFI)
摘要：The Markowitz problem consists of finding, in a financial market, a self-financing trading strategy whose final wealth has maximal mean and minimal variance. We study this in continuous time in a general semimartingale model and under cone constraints: trading strategies must take values in a (possibly random and time-dependent) closed cone. We first prove existence of a solution for convex constraints by showing that the space of constrained terminal gains, which is a space of stochastic inte...
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作者：Chen, Yu-Ting
作者单位：University of British Columbia
摘要：We study two of the simple rules on finite graphs under the death-birth updating and the imitation updating discovered by Ohtsuki, Hauert, Lieberman and Nowak [Nature 441 (2006) 502-505]. Each rule specifies a payoff-ratio cutoff point for the magnitude of fixation probabilities of the underlying evolutionary game between cooperators and defectors. We view the Markov chains associated with the two updating mechanisms as voter model perturbations. Then we present a first-order approximation for...
