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作者：Diaconis, Persi; Fulman, Jason; Holmes, Susan
作者单位：Stanford University; Stanford University; University of Southern California
摘要：Many casinos routinely use mechanical card shuffling machines. We were asked to evaluate a new product, a shelf shuffler. This leads to new probability, new combinatorics and to some practical advice which was adopted by the manufacturer. The interplay between theory, computing, and real-world application is developed.
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作者：Acciaio, B.; Beiglboeck, M.; Penkner, F.; Schachermayer, W.; Temme, J.
作者单位：University of Vienna; University of Perugia
摘要：We present a unified approach to Doob's L-p maximal inequalities for 1 <= p < infinity. The novelty of our method is that these martingale inequalities are obtained as consequences of elementary deterministic counterparts. The latter have a natural interpretation in terms of robust hedging. Moreover, our deterministic inequalities lead to new versions of Doob's maximal inequalities. These are best possible in the sense that equality is attained by properly chosen martingales.
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作者：Bertoin, Jean; Miermont, Gregory
作者单位：University of Zurich; Universite Paris Saclay
摘要：Consider the edge-deletion process in which the edges of some finite tree T are removed one after the other in the uniform random order. Roughly speaking, the cut-tree then describes the genealogy of connected components appearing in this edge-deletion process. Our main result shows that after a proper rescaling, the cut-tree of a critical Galton Watson tree with finite variance and conditioned to have size n, converges as n -> infinity to a Brownian continuum random tree (CRT) in the weak sen...
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作者：Galves, A.; Garcia, N. L.; Loecherbach, E.; Orlandi, E.
作者单位：Universidade Estadual de Campinas; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); CY Cergy Paris Universite; Roma Tre University
摘要：We consider a particle system on Z(d) with real state space and interactions of infinite range. Assuming that the rate of change is continuous we obtain a Kalikow-type decomposition of the infinite range change rates as a mixture of finite range change rates. Furthermore, if a high noise condition holds, as an application of this decomposition, we design a feasible perfect simulation algorithm to sample from the stationary process. Finally, the perfect simulation scheme allows us to forge an a...
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作者：Kardaras, Constantinos
作者单位：University of London; London School Economics & Political Science
摘要：A wealth-process set is abstractly defined to consist of nonnegative eking processes containing a strictly positive semimartingale and satisfying an intuitive re-balancing property. Under the condition of absence of arbitrage of the first kind, it is established that all wealth processes are semimartingales and that the closure of the wealth-process set in the Emery topology contains all optimal wealth processes.
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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：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：Dieker, A. B.; Gao, Xuefeng
作者单位：University System of Georgia; Georgia Institute of Technology
摘要：We study the positive recurrence of piecewise Ornstein-Uhlenbeck (OU) diffusion processes, which arise from many-server queueing systems with phase-type service requirements. These diffusion processes exhibit different behavior in two regions of the state space, corresponding to overload (service demand exceeds capacity) and underload (service capacity exceeds demand). The two regimes cause standard techniques for proving positive recurrence to fail. Using and extending the framework of common...
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作者：Griffin, Philip S.
作者单位：Syracuse University
摘要：We investigate the behavior of Levy processes with convolution equivalent Levy measures, up to the time of first passage over a high level u. Such problems arise naturally in the context of insurance risk where u is the initial reserve. We obtain a precise asymptotic estimate on the probability of first passage occurring by time T. This result is then used to study the process conditioned on first passage by time T. The existence of a limiting process as u -> infinity is demonstrated, which le...
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作者：Musacchio, John; Walrand, Jean
作者单位：University of California System; University of California Santa Cruz; University of California System; University of California Berkeley
摘要：We study a simple rate control scheme for a multiclass queuing network for which customers are partitioned into distinct flows that are queued separately at each station. The control scheme discards customers that arrive to the network ingress whenever any one of the flow's queues throughout the network holds more than a specified threshold number of customers. We prove that if the state of a corresponding fluid model tends to a set where the flow rates are equal to target rates, then there ex...
