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作者：Bank, Peter; Kauppila, Helena
作者单位：Technical University of Berlin; Columbia University
摘要：We develop a general theory of convex duality for certain singular control problems, taking the abstract results by Kramkov and Schachermayer [Ann. Appl Probab. 9 (1999) 904-950] for optimal expected utility from nonnegative random variables to the level of optimal expected utility from increasing, adapted controls. The main contributions are the formulation of a suitable duality framework, the identification of the problem's dual functional as well as the full duality for the primal and dual ...
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作者：Iyer, Srikanth; Vaze, Rahul
作者单位：Indian Institute of Science (IISC) - Bangalore; Tata Institute of Fundamental Research (TIFR)
摘要：In wireless networks, where each node transmits independently of other nodes in the network (the ALOHA protocol), the expected delay experienced by a packet until it is successfully received at any other node is known to be infinite for the signal-to-interference-plus-noise-ratio (SINR) model with node locations distributed according to a Poisson point process. Consequently, the information velocity, defined as the limit of the ratio of the distance to the destination and the time taken for a ...
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作者：Benaim, Michel; Bouguet, Florian; Cloez, Bertrand
作者单位：University of Neuchatel; Universite de Lorraine; INRAE; Institut Agro; Montpellier SupAgro; Universite de Montpellier; Universite de Lorraine; Universite de Lorraine; INRAE; Institut Agro; Montpellier SupAgro
摘要：In this work, we consider an inhomogeneous (discrete time) Markov chain and are interested in its long time behavior. We provide sufficient conditions to ensure that some of its asymptotic properties can be related to the ones of a homogeneous (continuous time) Markov process. Renowned examples such as a bandit algorithms, weighted random walks or decreasing step Euler schemes are included in our framework. Our results are related to functional limit theorems, but the approach differs from the...
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作者：Cai, Jiatu; Rosenbaum, Mathieu; Tankov, Peter
作者单位：Universite Paris Cite; Institut Polytechnique de Paris; ENSTA Paris; Ecole Polytechnique
摘要：We consider the problem of tracking a target whose dynamics is modeled by a continuous Ito semi-martingale. The aim is to minimize both deviation from the target and tracking efforts. We establish the existence of asymptotic lower bounds for this problem, depending on the cost structure. These lower bounds can be related to the time-average control of Brownian motion, which is characterized as a deterministic linear programming problem. A comprehensive list of examples with explicit expression...
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作者：Lalley, Steven; Su, Wei
作者单位：University of Chicago
摘要：We show that the contact process on a random d-regular graph initiated by a single infected vertex obeys the cutoff phenomenon in its supercritical phase. In particular, we prove that, when the infection rate is larger than the lower critical value of the contact process on the infinite d-regular tree, there are positive constants C, p depending on the infection rate such that for any epsilon > 0, when the number n of vertices is large then (a) at times t < (C - epsilon) log n the fraction of ...
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作者：Leobacher, Gunther; Szolgyenyi, Michaela
作者单位：University of Graz; Vienna University of Economics & Business; Johannes Kepler University Linz; Vienna University of Economics & Business
摘要：In this paper, we consider multidimensional stochastic differential equations (SDEs) with discontinuous drift and possibly degenerate diffusion coefficient. We prove an existence and uniqueness result for this class of SDEs and we present a numerical method that converges with strong order 1/2. Our result is the first one that shows existence and uniqueness as well as strong convergence for such a general class of SDEs. The proof is based on a transformation technique that removes the disconti...
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作者：Chatterjee, Sourav; Sen, Sanchayan
作者单位：Stanford University; McGill University
摘要：Kesten and Lee [Ann. AppL Probab. 6 (1996) 495-527] proved that the total length of a minimal spanning tree on certain random point configurations in R-d satisfies a central limit theorem. They also raised the question: how to make these results quantitative? Error estimates in central limit theorems satisfied by many other standard functionals studied in geometric probability are known, but techniques employed to tackle the problem for those functionals do not apply directly to the minimal sp...
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作者：Ghiglietti, Andrea; Vidyashankar, Anand N.; Rosenberger, William F.
作者单位：University of Milan; George Mason University
摘要：The generalized Polya urn (GPU) models and their variants have been investigated in several disciplines. However, typical assumptions made with respect to the GPU do not include urn models with a diagonal replacement matrix, which arise in several applications, specifically in clinical trials. To facilitate mathematical analyses of models in these applications, we introduce an adaptive randomly reinforced urn model that uses accruing statistical information to adaptively skew the urn proportio...
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作者：Bierme, Hermine; Durieu, Olivier; Wang, Yizao
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Poitiers; Centre National de la Recherche Scientifique (CNRS); University System of Ohio; University of Cincinnati
摘要：Recently, Hammond and Sheffield [Probab. Theory Related Fields 157 (2013) 691-719] introduced a model of correlated one-dimensional random walks that scale to fractional Brownian motions with long-range dependence. In this paper, we consider a natural generalization of this model to dimension d >= 2. We define a Z(d)-indexed random field with dependence relations governed by an underlying random graph with vertices Z(d), and we study the scaling limits of the partial sums of the random field o...
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作者：Dommers, S.; Den Hollander, F.; Jovanovski, O.; Nardi, F. R.
作者单位：Ruhr University Bochum; Leiden University - Excl LUMC; Leiden University; Eindhoven University of Technology
摘要：In this paper, we study metastable behaviour at low temperature of Glauber spin-flip dynamics on random graphs. We fix a large number of vertices and randomly allocate edges according to the configuration model with a prescribed degree distribution. Each vertex carries a spin that can point either up or down. Each spin interacts with a positive magnetic field, while spins at vertices that are connected by edges also interact with each other via a ferro-magnetic pair potential. We start from th...
