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作者：Dolera, Emanuele; Favaro, Stefano
作者单位：University of Pavia; University of Turin
摘要：This paper contributes to the study of the random number K-n of blocks in the random partition of {1, ..., n} induced by random sampling from the celebrated two parameter Poisson-Dirichlet process. For any alpha is an element of (0, 1) and theta > -alpha Pitman (Combinatorial Stochastic Processes (2006) Springer, Berlin) showed that n(-alpha) K-n ->(a.s.) S-alpha,S-theta as n -> +infinity, where the limiting random variable, referred to as Pitman's alpha-diversity, is distributed according to ...
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作者：Yan, Jun
作者单位：Stanford University
摘要：By extending (Adv. Math. 299 (2016) 396-450), we present a framework to calculate large deviations for nonlinear functions of independent random variables supported on compact sets in Banach spaces. Previous research on nonlinear large deviations has only focused on random variables supported on {-1, +1}(n), and accordingly we build theory for random variables with general distributions, increasing flexibility in the applications. As examples, we compute the large deviation rate functions for ...
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作者：Ngo, Hoang-Long; Taguchi, Dai
作者单位：Hanoi National University of Education; University of Osaka
摘要：We introduce a semi-implicit Euler-Maruyama approximation which preserves the noncolliding property for some class of noncolliding particle systems such as Dyson-Brownian motions, Dyson-Ornstein-Uhlenbeck processes and Brownian particle systems with nearest neighbor repulsion, and study its rates of convergence in both L-p-norm and pathwise sense.
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作者：Anastasiou, Andreas; Reinert, Gesine
作者单位：University of Cyprus; University of Oxford
摘要：In this paper, we give an explicit bound on the distance to chi-square for the likelihood ratio statistic when the data are realisations of independent and identically distributed random elements. To our knowledge, this is the first explicit bound which is available in the literature. The bound depends on the number of samples as well as on the dimension of the parameter space. We illustrate the bound with three examples: samples from an exponential distribution, samples from a normal distribu...
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作者：Bierme, Hermine; Desolneux, Agnes
作者单位：Universite de Poitiers; Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay
摘要：We introduce the level perimeter integral and the total curvature integral associated with a real-valued function f defined on the plane R-2, as integrals allowing to compute the perimeter of the excursion set of f above level t and the total (signed) curvature of its boundary for almost every level t. Thanks to the Gauss-Bonnet theorem, the total curvature is directly related to the Euler characteristic of the excursion set. We show that the level perimeter and the total curvature integrals c...
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作者：Kistler, Nicola; Schertzer, Adrien; Schmidt, Marius A.
作者单位：Goethe University Frankfurt; University of Basel
摘要：This is the second, and last paper in which we address the behavior of oriented first passage percolation on the hypercube in the limit of large dimensions. We prove here that the extremal process converges to a Cox process with exponential intensity. This entails, in particular, that the first passage time converges weakly to a random shift of the Gumbel distribution. The random shift, which has an explicit, universal distribution related to modified Bessel functions of the second kind, is th...
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作者：Shapira, Assaf
作者单位：Universite Paris Cite
摘要：We study two kinetically constrained models in a quenched random environment. The first model is a mixed threshold Fredrickson-Andersen model on Z(2), where the update threshold is either 1 or 2. The second is a mixture of the Fredrickson-Andersen 1-spin facilitated constraint and the North-East constraint in Z(2). We compare three time scales related to these models-the bootstrap percolation time for emptying the origin, the relaxation time of the kinetically constrained model, and the time f...
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作者：Mostovyi, Oleksii; Sirbu, Mihai
作者单位：University of Connecticut; University of Texas System; University of Texas Austin
摘要：We consider the problem of optimal consumption from labor income and investment in a general incomplete semimartingale market. The economic agent cannot borrow against future income, so the total wealth is required to be positive at (all or some) previous times. Under very general conditions, we show that an optimal consumption and investment plan exists and is unique, and provide a dual characterization in terms of an optional strong supermartingale deflator and a decreasing part, which charg...
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作者：Gamarnik, David; Tsitsiklis, John N.; Zubeldia, Martin
作者单位：Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT)
摘要：We consider the following distributed service model: jobs with unit mean, general distribution, and independent processing times arrive as a renewal process of rate lambda n, with 0 < lambda < 1, and are immediately dispatched to one of several queues associated with n identical servers with unit processing rate. We assume that the dispatching decisions are made by a central dispatcher endowed with a finite memory, and with the ability to exchange messages with the servers. We study the fundam...
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作者：Ankirchner, Stefan; Fromm, Alexander; Kruse, Thomas; Popier, Alexandre
作者单位：Friedrich Schiller University of Jena; Justus Liebig University Giessen; Le Mans Universite
摘要：We consider a variant of the basic problem of the calculus of variations, where the Lagrangian is convex and subject to randomness adapted to a Brownian filtration. We solve the problem by reducing it, via a limiting argument, to an unconstrained control problem that consists in finding an absolutely continuous process minimizing the expected sum of the Lagrangian and the deviation of the terminal state from a given target position. Using the Pontryagin maximum principle, we characterize a sol...
