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作者：Heiny, Johannes; Mikosch, Thomas; Yslas, Jorge
作者单位：Ruhr University Bochum; University of Copenhagen
摘要：We study point process convergence for sequences of i.i.d. random walks. The objective is to derive asymptotic theory for the extremes of these random walks. We show convergence of the maximum random walk to the Gumbel distribution under the existence of a (2 + delta)th moment. We make heavy use of precise large deviation results for sums of i.i.d. random variables. As a consequence, we derive the joint convergence of the off-diagonal entries in sample covariance and correlation matrices of a ...
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作者：Natarovskii, Viacheslav; Rudolf, Daniel; Sprungk, Bjoern
作者单位：University of Gottingen; Technical University Freiberg
摘要：We prove Wasserstein contraction of simple slice sampling for approximate sampling w.r.t. distributions with log-concave and rotational invariant Lebesgue densities. This yields, in particular, an explicit quantitative lower bound of the spectral gap of simple slice sampling. Moreover, this lower bound carries over to more general target distributions depending only on the volume of the (super-)level sets of their unnormalized density.
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作者：Friz, P. K.; Gassiat, P.; Pigato, P.
作者单位：Universite PSL; Universite Paris-Dauphine
摘要：We present a new methodology to analyze large classes of (classical and rough) stochastic volatility models, with special regard to short-time and small noise formulae for option prices. Our main tool is the theory of regularity structures, which we use in the form of Bayer et al. (Math. Finance 30 (2020) 782-832) In essence, we implement a Laplace method on the space of models (in the sense of Hairer), which generalizes classical works of Azencott and Ben Arous on path space and then Aida, In...
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作者：Lyberopoulos, Demetrios P.; Macheras, Nikolaos D.
作者单位：University of Piraeus
摘要：If a given aggregate process S is a mixed compound Poisson process under a probability measure P, we provide a characterization of all probability measures Q on the domain of P, such that P and Q are progressively equivalent and S remains a mixed compound Poisson process with improved properties. This result generalizes earlier work of Delbaen and Haezendonck (Insurance Math. Econom. 8 (1989) 269-277). Implications related to the computation of premium calculation principles in an insurance ma...
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作者：Lambert, Amaury; Pina, Veronica Miro; Schertzer, Emmanuel
作者单位：Universite Paris Cite; Sorbonne Universite; Institut National de la Sante et de la Recherche Medicale (Inserm); Universite PSL; College de France
摘要：We consider a Moran model with recombination in a haploid population of size N. At each birth event, with probability 1-rho R-N the offspring copies one parent's chromosome, and with probability rho R-N she inherits a chromosome that is a mosaic of both parental chromosomes. We assume that at time 0 each individual has her chromosome painted in a different color and we study the color partition of the chromosome that is asymptotically fixed in a large population, when we look at a portion of t...
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作者：Castiel, Eyal; Borst, Sem; Miclo, Laurent; Simatos, Florian; Whiting, Phil
作者单位：Universite de Toulouse; Institut Superieur de l'Aeronautique et de l'Espace (ISAE-SUPAERO); Eindhoven University of Technology; Universite de Toulouse; Universite Toulouse 1 Capitole; Toulouse School of Economics; Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Centre National de la Recherche Scientifique (CNRS); Macquarie University
摘要：We examine a queue-based random-access algorithm where activation and deactivation rates are adapted as functions of queue lengths. We establish its heavy traffic behavior on a complete interference graph, which turns out to be nonstandard in two respects: (1) the scaling depends on some parameter of the algorithm and is not the N/N-2 scaling usually found in functional central limit theorems; (2) the heavy traffic limit is deterministic. We discuss how this nonstandard behavior arises from th...
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作者：van der Hofstad, Remco; van Leeuwaarden, Johan S. H.; Stegehuis, Clara
作者单位：Eindhoven University of Technology; Tilburg University; University of Twente
摘要：Subgraphs reveal information about the geometry and functionalities of complex networks. For scale-free networks with unbounded degree fluctuations, we obtain the asymptotics of the number of times a small connected graph occurs as a subgraph or as an induced subgraph. We obtain these results by analyzing the configuration model with degree exponent tau epsilon (2, 3) and introducing a novel class of optimization problems. For any given subgraph, the unique optimizer describes the degrees of t...
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作者：Lucon, Eric; Poquet, Christophe
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet
摘要：We consider the long-time behavior of a population of mean-field oscillators modeling the activity of interacting excitable neurons in a large population. Each neuron is represented by its voltage and recovery variables, which are the solution to a FitzHugh-Nagumo system, and interacts with the rest of the population through a mean-field linear coupling, in the presence of noise. The aim of the paper is to study the emergence of collective oscillatory behaviors induced by noise and interaction...
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作者：Bakhtin, Yuri; Chen, Hong-Bin
作者单位：New York University
摘要：For a smooth vector field in a neighborhood of a critical point with all positive eigenvalues of the linearization, we consider the associated dynamics perturbed by white noise. Using Malliavin calculus tools, we obtain polynomial asymptotics for probabilities of atypically long exit times in the vanishing noise limit.
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作者：Vogrinc, Jure; Kendall, Wilfrid S.
作者单位：University of Warwick
摘要：For sufficiently smooth targets of product form it is known that the variance of a single coordinate of the proposal in RWM (random walk Metropolis) and MALA (Metropolis adjusted Langevin algorithm) should optimally scale as n(-1) and as n(-1/3) with dimension n, and that the acceptance rates should be tuned to 0.234 and 0.574. We establish counterexamples to demonstrate that smoothness assumptions of the order of C-1(R) for RWM and C-3(R) for MALA are indeed required if these scaling rates ar...
