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作者：Chatterjee, Sourav
作者单位：University of California System; University of California Berkeley
摘要：We introduce some applications of Stein's method in the high temperature analysis of spin glasses. Stein's method allows the direct analysis of the Gibbs measure without having to eate a cavity. Another advantage is that it gives limit theorems with total variation error bounds, although the bounds can be suboptimal. A surprising byproduct of our analysis is a relatively transparent explanation of the Thouless-Anderson-Palmer system of equations. Along the way, we develop Stein's method for mi...
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作者：Athreya, Siva R.; Swart, Jan M.
作者单位：Czech Academy of Sciences; Institute of Information Theory & Automation of the Czech Academy of Sciences; Indian Statistical Institute; Indian Statistical Institute Bangalore
摘要：We consider contact processes on the hierarchical group, where sites infect other sites at a rate depending on their hierarchical distance, and sites become healthy with a constant recovery rate. If the infection rates decay too fast as a function of the hierarchical distance, then we show that the critical recovery rate is zero. On the other hand, we derive sufficient conditions on the speed of decay of the infection rates for the process to exhibit a nontrivial phase transition between extin...
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作者：Kusuoka, Shigeo; Kuwada, Kazumasa; Tamura, Yozo
作者单位：Ochanomizu University; University of Tokyo; Keio University
摘要：The large deviation principle for stochastic line integrals along Brownian paths on a compact Riemannian manifold is studied. We regard them as a random map on a Sobolev space of 1-forms. We show that the differentiability order of the Sobolev space can be chosen to be almost independent of the dimension of the underlying space by assigning higher integrability on 1-forms. The large deviation is formulated for the joint distribution of stochastic line integrals and the empirical distribution o...
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作者：Bass, Richard F.; Burdzy, Krzysztof; Chen, Zhen-Qing; Hairer, Martin
作者单位：University of Washington; University of Washington Seattle; University of Connecticut; University of Warwick
摘要：Consider reflecting Brownian motion in a bounded domain in R-d that acquires drift in proportion to the amount of local time spent on the boundary of the domain. We show that the stationary distribution for the joint law of the position of the reflecting Brownian motion and the value of the drift vector has a product form. Moreover, the first component is uniformly distributed on the domain, and the second component has a Gaussian distribution. We also consider more general reflecting diffusio...
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作者：Chatterjee, Sourav; Pal, Soumik
作者单位：Cornell University; University of California System; University of California Berkeley
摘要：Consider a time-varying collection of n points on the positive real axis, modeled as Exponentials of n Brownian motions whose drift vector at every time point is determined by the relative ranks of the coordinate processes at that time. If at each time point we divide the points by their sum, under suitable assumptions the rescaled point process converges to a stationary distribution (depending on n and the vector of drifts) as time goes to infinity. This stationary distribution can be exactly...
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作者：Ji, Shaolin; Zhou, Xun Yu
作者单位：Shandong University; University of Oxford; Chinese University of Hong Kong
摘要：This paper is concerned with hypothesis tests for g-probabilities, a class of nonlinear probability measures. The problem is shown to be a special case of a general stochastic optimization problem where the objective is to choose the terminal state of certain backward stochastic differential equations so as to minimize a g-expectation. The latter is solved with a stochastic maximum principle approach. Neyman-Pearson type results are thereby derived for the original problem with both simple and...
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作者：Brown, Lawrence; Cai, Tony; Zhang, Ren; Zhao, Linda; Zhou, Harrison
作者单位：University of Pennsylvania; Yale University
摘要：We propose and implement a density estimation procedure which begins by turning density estimation into a nonparametric regression problem. This regression problem is created by binning the original observations into many small size bins, and by then applying a suitable form of root transformation to the binned data counts. In principle many common nonparametric regression estimators could then be applied to the transformed data. We propose use of a wavelet block thresholding estimator in this...
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作者：Gloter, Arnaud; Hoffmann, Marc
作者单位：Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Universite Gustave-Eiffel; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris-Est-Creteil-Val-de-Marne (UPEC)
摘要：We estimate a real-valued function f of d variables, subject to additive Gaussian perturbation at noise level epsilon > 0, under L-pi-loss, for pi >= 1. The main novelty is that f can have an extremely varying local smoothness, exhibiting a so-called multifractal behaviour. The results of Jaffard on the Frisch-Parisi conjecture suggest to link the singularity spectrum of f to Besov properties of the signal that can be handled by wavelet thresholding for denoising purposes. We prove that the op...
