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作者：Chetrite, Raphael; Diel, Roland; Lerasle, Matthieu
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite Cote d'Azur; Ton Duc Thang University; Ton Duc Thang University
摘要：We consider a Bradley-Terry model in random environment where each player faces each other once. More precisely, the strengths of the players are assumed to be random and we study the influence of their distributions on the asymptotic number of potential winners. First, we prove that under moment and convexity conditions, the asymptotic probability that the best player wins is 1. The convexity condition is natural when the distribution of strengths is unbounded and, in the bounded case, when t...
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作者：Durmus, Alain; Moulines, Eric
作者单位：IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom Paris; Centre National de la Recherche Scientifique (CNRS); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Institut Polytechnique de Paris; ENSTA Paris; Ecole Polytechnique
摘要：In this paper, we study a method to sample from a target distribution pi over R-d having a positive density with respect to the Lebesgue measure, known up to a normalisation factor. This method is based on the Euler discretization of the overdamped Langevin stochastic differential equation associated with pi. For both constant and decreasing step sizes in the Euler discretization, we obtain nonasymptotic bounds for the convergence to the target distribution pi in total variation distance. A pa...
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作者：Kolodziejek, Bartosz
作者单位：Warsaw University of Technology
摘要：In this paper, we show under weak assumptions that for R = (d) 1 + M-1 M1M2 + . . ., where P(M is an element of [0, 1]) = 1 and M-i are independent copies of M, we have lnP(R > x) similar to CxlnP(M > 1 - 1/x) as x -> infinity. The constant C is given explicitly and its value depends on the rate of convergence of 1nP(M > 1 - 1/x). Random variable R satisfies the stochastic equation R 1 + MR with M and R independent, thus this result fits into the study of tails of iterated random equations, or...
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作者：Braverman, Anton; Dai, J. G.
作者单位：Cornell University
摘要：We consider M/Ph/n + M queueing systems in steady state. We prove that the Wasserstein distance between the stationary distribution of the normalized system size process and that of a piecewise Ornstein Uhlenbeck (OU) process is bounded by C/root T., where the constant C is independent of the arrival rate A and the number of servers n as long as they are in the HalfinWhitt parameter regime. For each integer m > 0, we also establish a similar bound for the difference of the mth steady-state mom...
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作者：Chen, Guan-Yu; Hsu, Jui-Ming; Sheu, Yuan-Chung
作者单位：National Yang Ming Chiao Tung University
摘要：In this article, we considers reversible Markov chains of which L-2-distances can be expressed in terms of Laplace transforms. The cutoff of Laplace transforms was first discussed by Chen and Saloff-Coste in [J. Funct. Anal. 258 (2010) 2246-2315], while we provide here a completely different pathway to analyze the L-2-distance. Consequently, we obtain several considerably simplified criteria and this allows us to proceed advanced theoretical studies, including the comparison of cutoffs between...
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作者：Jarai, Antal A.
作者单位：University of Bath
摘要：We study the following game on a finite graph G = (V,E). Each edge e is an element of E starts with an integer value n(e) >= 0, and we write n = Sigma eE n(e). At time t, 1 <= t <= n, a uniformly random vertex v is an element of V is generated, and one of the edges f incident with v must be selected. The value of f is then decreased by 1. There is a unit final reward if the configuration (0,...,0) is reached. Our main result is that there is a phase transition: as n -> infinity, the expected r...
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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...
