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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：Hermon, Jonathan; Salez, Justin
作者单位：University of British Columbia; Universite PSL; Universite Paris-Dauphine; Universite PSL
摘要：We resolve a long-standing conjecture of Wilson (Ann. Appl. Probab. 14 (2004) 274-325), reiterated by Oliveira (2016), asserting that the mixing time of the interchange process with unit edge rates on the n-dimensional hyper-cube is of order n. This follows from a sharp inequality established at the level of Dirichlet forms, from which we also deduce that macroscopic cycles emerge in constant time, and that the log-Sobolev constant of the exclusion process is of order 1. Beyond the hypercube, ...
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作者：Sun, Jingrui; Xiong, Jie; Yong, Jiongmin
作者单位：Southern University of Science & Technology; State University System of Florida; University of Central Florida
摘要：This paper is concerned with a stochastic linear-quadratic optimal control problem in a finite time horizon, where the coefficients of the control system are allowed to be random, and the weighting matrices in the cost functional are allowed to be random and indefinite. It is shown, with a Hilbert space approach, that for the existence of an open-loop optimal control, the convexity of the cost functional (with respect to the control) is necessary; and the uniform convexity, which is slightly s...
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作者：Tomasevic, Milica
作者单位：Centre National de la Recherche Scientifique (CNRS); Institut Polytechnique de Paris; Ecole Polytechnique
摘要：Recently, we proposed a new stochastic interpretation of the parabolic-parabolic Keller-Segel system without cut-off via a McKean-Vlasov stochastic process. The process was defined through an original type of interaction kernel which involved, in a singular way, all its past time marginal distributions. In the present paper, we study this McKean-Vlasov representation in the two-dimensional case. In this setting, there exists a possibility of a blow-up in finite time for the Keller-Segel system...
