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作者：Iyer, Gautam; Leger, Nicholas; Pego, Robert L.
作者单位：Carnegie Mellon University
摘要：We investigate the well-posedness and asymptotic self-similarity of solutions to a generalized Smoluchowski coagulation equation recently introduced by Bertoin and Le Gall in the context of continuous-state branching theory. In particular, this equation governs the evolution of the Levy measure of a critical continuous-state branching process which becomes extinct (i.e., is absorbed at zero) almost surely. We show that a nondegenerate scaling limit of the Levy measure (and the process) exists ...
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作者：Kardaras, Constantinos
作者单位：University of London; London School Economics & Political Science
摘要：In this paper, a study of random times on filtered probability spaces is undertaken. The main message is that, as long as distributional properties of optional processes up to the random time are involved, there is no loss of generality in assuming that the random time is actually a randomised stopping time. This perspective has advantages in both the theoretical and practical study of optional processes up to random times. Applications are given to financial mathematics, as well as to the stu...
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作者：Berti, Patrizia; Crimaldi, Irene; Pratelli, Luca; Rigo, Pietro
作者单位：Universita di Modena e Reggio Emilia; IMT School for Advanced Studies Lucca; University of Pavia
摘要：The three-parameter Indian buffet process is generalized. The possibly different role played by customers is taken into account by suitable (random) weights. Various limit theorems are also proved for such generalized Indian buffet process. Let L-n be the number of dishes experimented by the first n customers, and let (K) over bar (n)= (1/n) Sigma(n)(i=1) K-i where K-i is the number of dishes tried by customer i. The asymptotic distributions of L-n and (K) over bar (n), suitably centered and s...
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作者：Moyal, P.
作者单位：Universite de Technologie de Compiegne
摘要：We propose an explicit construction of a stationary solution for a stochastic recursion of the form X o theta = phi(X) on a partially-ordered Polish space, when the monotonicity of phi is not assumed. Under certain conditions, we show that an extension of the original probability space exists, on which a solution is well defined, and construct explicitly this extension using a randomized contraction technique. We then provide conditions for the existence of a solution on the original space. We...
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作者：Zhu, Lingjiong
作者单位：New York University
摘要：Hawkes process is a class of simple point processes that is self-exciting and has clustering effect. The intensity of this point process depends on its entire past history. It has wide applications in finance, neuroscience and many other fields. In this paper, we study the large deviations for nonlinear Hawkes processes. The large deviations for linear Hawkes processes has been studied by Bordenave and Torrisi. In this paper, we prove first a large deviation principle for a special class of no...
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作者：Abdullah, Mohammed; Cooper, Colin; Draief, Moez
作者单位：University of Birmingham; University of London; King's College London; Imperial College London
摘要：We study the SIR epidemic model with infections carried by k particles making independent random walks on a random regular graph. Here we assume k <= n(epsilon), where n is the number of vertices in the random graph, and epsilon is some sufficiently small constant. We give an edge-weighted graph reduction of the dynamics of the process that allows us to apply standard results of Erdos-Renyi random graphs on the particle set. In particular, we show how the parameters of the model give two thres...
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作者：Huber, Mark
作者单位：Claremont Colleges; Claremont McKenna College; Claremont Graduate University
摘要：Consider a family of distributions {pi(beta)} where X similar to pi(beta) means that P(X = x) = exp(-beta H(x))/Z(beta). Here Z(beta) is the proper normalizing constant, equal to Sigma(x) exp(-beta H(x)). Then {pi(beta)} is known as a Gibbs distribution, and Z(beta) is the partition function. This work presents a new method for approximating the partition function to a specified level of relative accuracy using only a number of samples, that is, O(ln(Z(beta) ln(ln(Z(beta)))) when Z(0) >= 1. Th...
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作者：Biskup, Marek; Richthammer, Thomas
作者单位：University of California System; University of California Los Angeles; University of South Bohemia Ceske Budejovice; University of Hildesheim; University of Hildesheim
摘要：We consider Gibbs distributions on permutations of a locally finite infinite set X subset of R, where a permutation sigma of X is assigned (formal) energy Sigma(x is an element of X) V(sigma(x) - x). This is motivated by Feynman's path representation of the quantum Bose gas; the choice X := Z and V(x) := alpha x(2) is of principal interest. Under suitable regularity conditions on the set X and the potential V, we establish existence and a full classification of the infinite-volume Gibbs measur...
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作者：Andrieu, Christophe; Vihola, Matti
作者单位：University of Bristol; University of Oxford
摘要：We study convergence properties of pseudo-marginal Markov chain Monte Carlo algorithms (Andrieu and Roberts [Ann. Statist. 37 (2009) 697-725]). We find that the asymptotic variance of the pseudo-marginal algorithm is always at least as large as that of the marginal algorithm. We show that if the marginal chain admits a (right) spectral gap and the weights (normalised estimates of the target density) are uniformly bounded, then the pseudo-marginal chain has a spectral gap. In many cases, a simi...
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作者：Bayati, Mohsen; Lelarge, Marc; Montanari, Andrea
作者单位：Stanford University; Inria; Universite PSL; Ecole Normale Superieure (ENS); Stanford University; Stanford University
摘要：We consider a class of nonlinear mappings F-A,F-N in R-N indexed by symmetric random matrices A is an element of R-NxN with independent entries. Within spin glass theory, special cases of these mappings correspond to iterating the TAP equations and were studied by Bolthausen [Comm. Math. Phys. 325 (2014) 333-366]. Within information theory, they are known as approximate message passing algorithms. We study the high-dimensional (large N) behavior of the iterates of F for polynomial functions F,...
