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作者：Lambert, Amaury; Popovic, Lea
作者单位：Sorbonne Universite; Concordia University - Canada
摘要：We define a doubly infinite, monotone labeling of Bienayme-Galton-Watson (BOW) genealogies. The genealogy of the current generation backwards in time is uniquely determined by the coalescent point process (At; i >= 1), where A(i) is the coalescence time between individuals i and i + 1. There is a Markov process of point measures (8(i); i >= 1) keeping track of more ancestral relationships, such that A(i) is also the first point mass of B-i. This process of point measures is also closely relate...
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作者：Soner, H. Mete; Touzi, Nizar; Zhang, Jianfeng
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich; Swiss Finance Institute (SFI); Institut Polytechnique de Paris; Ecole Polytechnique; University of Southern California
摘要：This paper provides a new formulation of second order stochastic target problems introduced in [SIAM J. Control Optim. 48 (2009) 2344-2365] by modifying the reference probability so as to allow for different scales. This new ingredient enables us to prove a dual formulation of the target problem as the supremum of the solutions of standard backward stochastic differential equations. In particular, in the Markov case, the dual problem is known to be connected to a fully nonlinear, parabolic par...
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作者：Addario-Berry, Louigi; Ford, Kevin
作者单位：McGill University; University of Illinois System; University of Illinois Urbana-Champaign
摘要：We determine, to within 0(1), the expected minimal position at level n in certain branching random walks. The walks under consideration have displacement vector (nu 1, nu 2, ... ), where each vi is the sum of j independent Exponential(1) random variables and the different vi need not be independent. In particular, our analysis applies to the Poisson-Dirichlet branching random walk and to the Poisson-weighted infinite tree. As a corollary, we also determine the expected height of a random recur...
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作者：Bertini, Lorenzo; Faggionato, Alessandra; Gabrielli, Davide
作者单位：Sapienza University Rome; University of L'Aquila
摘要：We consider a lattice gas on the discrete d-dimensional torus (Z/NZ)(d) with a generic translation invariant, finite range interaction satisfying a uniform strong mixing condition. The lattice gas performs a Kawasaki dynamics in the presence of a weak external field E/N. We show that, under diffusive rescaling, the hydrodynamic behavior of the lattice gas is described by a nonlinear driven diffusion equation. We then prove the associated dynamical large deviation principle. Under suitable assu...
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作者：Kaspi, Haya; Ramanan, Kavita
作者单位：Technion Israel Institute of Technology; Brown University
摘要：This paper studies a queueing system in which customers with independent and identically distributed service times arrive to a queue with many servers and enter service in the order of arrival. The state of the system is represented by a process that describes the total number of customers in the system, and a measure-valued process that keeps track of the ages of customers in service, leading to a Markovian description of the dynamics. Under suitable assumptions, a functional central limit th...
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作者：Giesecke, Kay; Spiliopoulos, Konstantinos; Sowers, Richard B.
作者单位：Stanford University; Brown University; University of Illinois System; University of Illinois Urbana-Champaign
摘要：We develop a dynamic point process model of correlated default timing in a portfolio of firms, and analyze typical default profiles in the limit as the size of the pool grows. In our model, a firm defaults at a stochastic intensity that is influenced by an idiosyncratic risk process, a systematic risk process common to all firms, and past defaults. We prove a law of large numbers for the default rate in the pool, which describes the typical behavior of defaults.
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作者：Durrett, Rick
作者单位：Duke University
摘要：In order to analyze data from cancer genome sequencing projects, we need to be able to distinguish causative, or driver, mutations from passenger mutations that have no selective effect. Toward this end, we prove results concerning the frequency of neutural mutations in exponentially growing multitype branching processes that have been widely used in cancer modeling. Our results yield a simple new population genetics result for the site frequency spectrum of a sample from an exponentially grow...
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作者：Latuszynski, Krzysztof; Roberts, Gareth O.; Rosenthal, Jeffrey S.
作者单位：University of Warwick; University of Toronto
摘要：We consider various versions of adaptive Gibbs and Metropolis-within-Gibbs samplers, which update their selection probabilities (and perhaps also their proposal distributions) on the fly during a run by learning as they go in an attempt to optimize the algorithm. We present a cautionary example of how even a simple-seeming adaptive Gibbs sampler may fail to converge. We then present various positive results guaranteeing convergence of adaptive Gibbs samplers under certain conditions.
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作者：Ruggiero, Matteo; Walker, Stephen G.; Favaro, Stefano
作者单位：University of Turin; University of Kent
摘要：The infinitely-many-neutral-alleles model has recently been extended to a class of diffusion processes associated with Gibbs partitions of two-parameter Poisson-Dirichlet type. This paper introduces a family of infinite-dimensional diffusions associated with a different subclass of Gibbs partitions, induced by normalized inverse-Gaussian random probability measures. Such diffusions describe the evolution of the frequencies of infinitely-many types together with the dynamics of the time-varying...
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作者：Xu, Zuo Quan; Zhou, Xun Yu
作者单位：Hong Kong Polytechnic University; University of Oxford; University of Oxford; Chinese University of Hong Kong
摘要：We formulate an optimal stopping problem for a geometric Brownian motion where the probability scale is distorted by a general nonlinear function. The problem is inherently time inconsistent due to the Choquet integration involved. We develop a new approach, based on a reformulation of the problem where one optimally chooses the probability distribution or quantile function of the stopped state. An optimal stopping time can then be recovered from the obtained distribution/quantile function, ei...
