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作者：Pitman, Jim; Yakubovich, Yuri
作者单位：University of California System; University of California Berkeley; Saint Petersburg State University; Saint Petersburg State University
摘要：We describe the distribution of frequencies ordered by sample values in a random sample of size n from the two parameter GEM(alpha, theta) random discrete distribution on the positive integers. These frequencies are a (size-alpha)-biased random permutation of the sample frequencies in either ranked order, or in the order of appearance of values in the sampling process. This generalizes a well-known identity in distribution due to Donnelly and Tavare [Adv. in Appl. Probab.18 (1986) 1-19] for al...
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作者：Guo, Heng; Jerrum, Mark
作者单位：University of Edinburgh; University of London; Queen Mary University London
摘要：We show that the mixing time of Glauber (single edge update) dynamics for the random cluster model at q = 2 on an arbitrary n-vertex graph is bounded by a polynomial in n. As a consequence, the Swendsen Wang algorithm for the ferromagnetic Ising model at any temperature also has a polynomial mixing time bound.
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作者：Qian, Zhongmin; Xu, Mingyu
作者单位：University of Oxford; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS
摘要：In this article, we study a class of reflected backward stochastic differential equations (introduced in El Karoui et al. [Ann. Probab. 25 (1997) 702-737], RBSDE for short) with nonlinear resistance by means of Skorohod's equation. The advantage of this approach lies in its pathwise nature and, therefore, provides additional information about solutions of RBSDE. As an application of our approach, we will consider reflected backward problems with resistance as well. This class of RBSDEs possess...
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作者：Doney, R. A.; Griffin, Philip S.
作者单位：University of Manchester; Syracuse University
摘要：The reflected process of a random walk or Levy process arises in many areas of applied probability, and a question of particular interest is how the tail of the distribution of the heights of the excursions away from zero behaves asymptotically. The Levy analogue of this is the tail behaviour of the characteristic measure of the height of an excursion. Apparently, the only case where this is known is when Cramer's condition hold. Here, we establish the asymptotic behaviour for a large class of...
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作者：Cetin, Umut
作者单位：University of London; London School Economics & Political Science
摘要：We develop a new class of path transformations for one-dimensional diffusions that are tailored to alter their long-run behaviour from transient to recurrent or vice versa. This immediately leads to a formula for the distribution of the first exit times of diffusions, which is recently characterised by Karatzas and Ruf [Probab. Theory Related Fields 164 (2016) 1027-1069] as the minimal solution of an appropriate Cauchy problem under more stringent conditions. A particular limit of these transf...
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作者：Ma, Ruibo; Durrett, Rick
作者单位：Duke University
摘要：We study an evolutionary game in which a producer at x gives birth at rate 1 to an offspring sent to a randomly chosen point in x + N-c, while a cheater at x gives birth at rate lambda > 1 times the fraction of producers in x + N-d and sends its offspring to a randomly chosen point in x + N-c. We first study this game on the d-dimensional torus (Z mod L)(d) with N-d = (Z mod L)(d) and N-c = the 2d nearest neighbors. If we let L -> infinity then t -> infinity the fraction of producers converges...
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作者：Rodosthenous, Neofytos; Zhang, Hongzhong
作者单位：University of London; Queen Mary University London; Columbia University
摘要：We study the optimal stopping of an American call option in a random time-horizon under exponential spectrally negative Levy models. The random time-horizon is modeled as the so-called Omega default clock in insurance, which is the first time when the occupation time of the underlying Levy process below a level y, exceeds an independent exponential random variable with mean 1/q > 0. We show that the shape of the value function varies qualitatively with different values of q and y. In particula...
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作者：Chatterjee, Shirshendu; Zeitouni, Ofer
作者单位：City University of New York (CUNY) System; City College of New York (CUNY); Weizmann Institute of Science; New York University
摘要：We consider the searching for a trail in a maze composite hypothesis testing problem, in which one attempts to detect an anomalous directed path in a lattice 2D box of side n based on observations on the nodes of the box. Under the signal hypothesis, one observes independent Gaussian variables of unit variance at all nodes, with zero mean off the anomalous path and mean mu(n) on it. Under the null hypothesis, one observes i.i.d. standard Gaussians on all nodes. Arias-Castro et al. [Ann. Statis...
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作者：Foondun, Mohammud; Joseph, Mathew; Li, Shiu-Tang
作者单位：University of Strathclyde; University of Sheffield; Utah System of Higher Education; University of Utah
摘要：We show that a large class of stochastic heat equations can be approximated by systems of interacting stochastic differential equations. As a consequence, we prove various comparison principles extending earlier works of [Stoch. Stoch. Rep. 37 (1991) 225-245] and [Ann. Probab. 45 (2017) 377403] among others. Among other things, our results enable us to obtain sharp estimates on the moments of the solution. A main technical ingredient of our method is a local limit theorem which is of independe...
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作者：Gulikers, Lennart; Lelarge, Marc; Massoulie, Laurent
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; Universite PSL; Ecole Normale Superieure (ENS)
摘要：We consider the Degree-Corrected Stochastic Block Model (DC-SBM): a random graph on n nodes, having i.i.d. weights (phi u)(u)(n)=i (possibly heavytailed), partitioned into q >= 2 asymptotically equal-sized clusters. The model parameters are two constants a, b > 0 and the finite second moment of the weights Phi((2)). Vertices u and v are connected by an edge with probability phi u phi v/na when they are in the same class and with probability phi u phi v/nb otherwise. We prove that it is informa...
