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作者：Atar, Rami; Cohen, Asaf
作者单位：Technion Israel Institute of Technology; University of Michigan System; University of Michigan
摘要：A multi-class single-server queueing model with finite buffers, in which scheduling and admission of customers are subject to control, is studied in the moderate deviation heavy traffic regime. A risk-sensitive cost set over a finite time horizon [0, T] is considered. The main result is the asymptotic optimality of a control policy derived via an underlying differential game. The result is the first to address a queueing control problem at the moderate deviation regime that goes beyond models ...
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作者：Bobrowski, Omer; Kahle, Matthew; Skraba, Primoz
作者单位：Duke University; University System of Ohio; Ohio State University; Slovenian Academy of Sciences & Arts (SASA); Jozef Stefan Institute; University of Primorska; Technion Israel Institute of Technology
摘要：We initiate the study of persistent homology of random geometric simplicial complexes. Our main interest is in maximally persistent cycles of degree-k in persistent homology, for a either the Cech or the Vietoris-Rips filtration built on a uniform Poisson process of intensity n in the unit cube [0, 1](d). This is a natural way of measuring the largest k-dimensional hole in a random point set. This problem is in the intersection of geometric probability and algebraic topology, and is naturally ...
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作者：Burzoni, Matte; Frittelli, Marco; Maggis, Marco
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich; University of Milan
摘要：In a model-free discrete time financial market, we prove the superhedging duality theorem, where trading is allowed with dynamic and semistatic strategies. We also show that the initial cost of the cheapest portfolio that dominates a contingent claim on every possible path omega is an element of Omega, might be strictly greater than the upper bound of the no-arbitrage prices. We therefore characterize the subset of trajectories on which this duality gap disappears and prove that it is an analy...
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作者：Bierkens, Joris; Roberts, Gareth
作者单位：Delft University of Technology; University of Warwick
摘要：In Turitsyn, Chertkov and Vucelja [Phys. D 240 (2011) 410-414] a nonreversible Markov Chain Monte Carlo (MCMC) method on an augmented state space was introduced, here referred to as Lifted Metropolis Hastings (LMH). A scaling limit of the magnetization process in the Curie Weiss model is derived for LMH, as well as for Metropolis Hastings (MH). The required jump rate in the high (supercritical) temperature regime equals n(1/2) for LMH, which should be compared to n for MH. At the critical temp...
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作者：Kaellblad, Sigrid; Tan, Xiaolu; Touzi, Nizar
作者单位：Technische Universitat Wien; Universite PSL; Universite Paris-Dauphine; Centre National de la Recherche Scientifique (CNRS); Institut Polytechnique de Paris; ENSTA Paris; Ecole Polytechnique
摘要：We consider the optimal Skorokhod embedding problem (SEP) given full marginals over the time interval [0,1]. The problem is related to the study of extremal martingales associated with a peacock (process increasing in convex order, by Hirsch, Profeta, Roynette and Yor [Peacocks and Associated Martingales, with Explicit Constructions (2011), Springer, Milan]). A general duality result is obtained by convergence techniques. We then study the case where the reward function depends on the maximum ...
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作者：Kabluchko, Zakhar; Marynych, Alexander; Sulzbach, Henning
作者单位：University of Munster; Ministry of Education & Science of Ukraine; Taras Shevchenko National University of Kyiv; McGill University
摘要：We prove an asymptotic Edgeworth expansion for the profiles of certain random trees including binary search trees, random recursive trees and plane-oriented random trees, as the size of the tree goes to infinity. All these models can be seen as special cases of the one-split branching random walk for which we also provide an Edgeworth expansion. These expansions lead to new results on mode, width and occupation numbers of the trees, settling several open problems raised in Devroye and Hwang [A...
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作者：Juengel, Ansgar; Yue, Wen
作者单位：Technische Universitat Wien
摘要：Discrete convex Sobolev inequalities and Beckner inequalities are derived for time-continuous Markov chains on finite state spaces. Beckner inequalities interpolate between the modified logarithmic Sobolev inequality and the Poincare inequality. Their proof is based on the Bakry-Emery approach and on discrete Bochner-type inequalities established by Caputo, Dai Pra and Posta and recently extended by Fathi and Maas for logarithmic entropies. The abstract result for convex entropies is applied t...
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作者：Dinh, Vu; Matsen, Frederick A.
作者单位：Fred Hutchinson Cancer Center
摘要：By fixing all parameters in a phylogenetic likelihood model except for one branch length, one obtains a one-dimensional likelihood function. In this work, we introduce a mathematical framework to characterize the shapes of such one-dimensional phylogenetic likelihood functions. This framework is based on analyses of algebraic structures on the space of all frequency patterns with respect to a polynomial representation of the likelihood functions. Using this framework, we provide conditions und...
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作者：Johnson, Peter; Peskir, Goran
作者单位：University of Manchester
摘要：Consider the motion of a Brownian particle that initially takes place in a two-dimensional plane and then after some random/unobservable time continues in the three-dimensional space. Given that only the distance of the particle to the origin is being observed, the problem is to detect the time at which the particle departs from the plane as accurately as possible. We solve this problem in the most uncertain scenario when the random/unobservable time is (i) exponentially distributed and (ii) i...
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作者：Moyal, Pascal; Perry, Ohad
作者单位：Universite de Technologie de Compiegne; Northwestern University
摘要：A matching queue is described via a graph, an arrival process and a matching policy. Specifically, to each node in the graph there is a corresponding arrival process of items, which can either be queued or matched with queued items in neighboring nodes. The matching policy specifies how items are matched whenever more than one matching is possible. Given the matching graph and the matching policy, the stability region of the system is the set of intensities of the arrival processes rendering t...
