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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：Chen, Louis H. Y.; Rollin, Adrian; Xia, Aihua
作者单位：National University of Singapore; National University of Singapore; University of Melbourne
摘要：We establish a general Berry-Esseen type bound which gives optimal bounds in many situations under suitable moment assumptions. By combining the general bound with Palm theory, we deduce a new error bound for assessing the accuracy of normal approximation to statistics arising from random measures, including stochastic geometry. We illustrate the use of the bound in four examples: completely random measures, excursion random measure of a locally dependent random process, and the total edge len...
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作者：Matoussi, Anis; Possamai, Dylan; Zhou, Chao
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; Le Mans Universite; Swiss Federal Institutes of Technology Domain; ETH Zurich; National University of Singapore
摘要：The aim of this short note is to fill in a gap in our earlier paper (Ann. Appl. Probab. 23 (2013) 2420-2457) on 2BSDEs with reflections, and to explain how to correct the subsequent results in the second paper (Stochastic Process. Appl. 124 (2014) 2281-2321). We also provide more insight on the properties of 2RBSDEs, in the light of the recent contributions (Li and Peng (2017); Soumana Hima (2017)) in the so-called G-framework.
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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：Bramson, Maury; Gray, Lawrence F.
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：The majority vote process was one of the first interacting particle systems to be investigated. It can be described briefly as follows. There are two possible opinions at each site of a graph G. At rate 1 - epsilon, the opinion at a site aligns with the majority opinion at its neighboring sites and, at rate epsilon, the opinion at a site is randomized due to noise, where epsilon is an element of [0, 1] is a parameter. Despite the simple dynamics of the majority vote process, its equilibrium be...
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作者：Hu, Yaozhong; Liu, Yanghui; Nualart, David
作者单位：University of Alberta; City University of New York (CUNY) System; Baruch College (CUNY); University of Kansas
摘要：We study the Crank-Nicolson scheme for stochastic differential equations (SDEs) driven by a multidimensional fractional Brownian motion with Hurst parameterH > 1/2. It is well known that for ordinary differential equations with proper conditions on the regularity of the coefficients, the Crank-Nicolson scheme achieves a convergence rate of n(-2), regardless of the dimension. In this paper we show that, due to the interactions between the driving processes, the corresponding Crank-Nicolson sche...
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作者：Shao, Qi-Man; Zhang, Mengchen; Zhang, Zhuo-Song
作者单位：Southern University of Science & Technology; Chinese University of Hong Kong; Hong Kong University of Science & Technology; National University of Singapore
摘要：A Cramer-type moderate deviation theorem quantifies the relative error of the tail probability approximation. It provides a criterion whether the limiting tail probability can be used to estimate the tail probability under study. Chen, Fang and Shao (2013) obtained a general Cramer-type moderate result using Stein's method when the limiting was a normal distribution. In this paper, Cramer-type moderate deviation theorems are established for nonnormal approximation under a general Stein identit...
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作者：Henry-Labordere, Pierre; Touzi, Nizar
作者单位：Universite Paris Cite; Institut Polytechnique de Paris; ENSTA Paris
摘要：We provide probabilistic representations of the solution of some semi-linear hyperbolic and high-order PDEs based on branching diffusions. These representations pave the way for an approximation of the solution by the standard Monte Carlo method, whose error estimate is controlled by the standard central limit theorem, thus partly bypassing the curse of dimensionality. We illustrate the numerical implications in the context of some popular PDEs in physics such as nonlinear Klein-Gordon equatio...
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作者：Jaber, Eduardo Abi; Miller, Enzo; Pham, Huyen
作者单位：Universite Paris Cite
摘要：We provide an exhaustive treatment of linear-quadratic control problems for a class of stochastic Volterra equations of convolution type, whose kernels are Laplace transforms of certain signed matrix measures which are not necessarily finite. These equations are in general neither Markovian nor semimartingales, and include the fractional Brownian motion with Hurst index smaller than 1/2 as a special case. We establish the correspondence of the initial problem with a possibly infinite dimension...
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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...
