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作者：Wang, Neng-Yi; Wu, Liming
作者单位：Huazhong University of Science & Technology; Universite Clermont Auvergne (UCA); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：This paper is the discrete time counterpart of the previous work in the continuous time case by Guillin, Leonard, the second named author and Yao [Probab. Theory Related Fields 144 (2009), 669-695]. We investigate the following transport-information TvI inequality: alpha(T-v(nu, mu)) <= I(nu vertical bar P, mu) for all probability measures nu on some metric space (X, d), where mu is an invariant and ergodic probability measure of some given transition kernel P (x, dy), T-v(nu, mu) is some tran...
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作者：Benjamini, Itai; Fontes, Luiz Renato; Hermon, Jonathan; Machado, Fabio Prates
作者单位：Weizmann Institute of Science; Universidade de Sao Paulo; University of Cambridge
摘要：We study a system of random walks, known as the frog model, starting from a profile of independent Poisson(lambda) particles per site, with one additional active particle planted at some vertex o of a finite connected simple graph G = (V, E). Initially, only the particles occupying o are active. Active particles perform t is an element of N boolean OR {infinity} steps of the walk they picked before vanishing and activate all inactive particles they hit. This system is often taken as a model fo...
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作者：Allan, Andrew L.; Cohen, Samuel N.
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich; University of Oxford
摘要：We study the problem of pathwise stochastic optimal control, where the optimization is performed for each fixed realisation of the driving noise, by phrasing the problem in terms of the optimal control of rough differential equations. We investigate the degeneracy phenomenon induced by directly controlling the coefficient of the noise term, and propose a simple procedure to resolve this degeneracy whilst retaining dynamic programming As an application, we use pathwise stochastic control in the...
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作者：Banerjee, Sayan; Budhiraja, Amarjit
作者单位：University of North Carolina; University of North Carolina Chapel Hill
摘要：We obtain rates of convergence to stationarity in L-1-Wasserstein distance for a d-dimensional reflected Brownian motion (RBM) in the nonnegative orthant that are explicit in the dimension and the system parameters. The results are then applied to a class of RBMs considered in (Blanchet and Xinyun (2016)) and to rank-based diffusions including the Atlas model. In both cases, we obtain explicit rates and bounds on relaxation times. In the first case we improve the relaxation time estimates of O...
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作者：Hutzenthaler, Martin; Pieper, Daniel
作者单位：University of Duisburg Essen
摘要：Propagation of chaos is a well-studied phenomenon and shows that weakly interacting diffusions may become independent as the system size converges to infinity. Most of the literature focuses on the case of exchangeable systems where all involved diffusions have the same distribution and are of the same size. In this paper, we analyze the case where only a few diffusions start outside of an accessible trap. Our main result shows that in this sparse regime the system of weakly interacting diffus...
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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：He, Yukun
作者单位：University of Zurich
摘要：We consider a class of sparse random matrices, which includes the adjacency matrix of Erdos-Renyi graphs G(N, p) for p is an element of [N epsilon-1, N-epsilon]. We identify the joint limiting distributions of the eigenvalues away from 0 and the spectral edges. Our result indicates that unlike Wigner matrices, the eigenvalues of sparse matrices satisfy central limit theorems with normalization N root p. In addition, the eigenvalues fluctuate simultaneously: the correlation of two eigenvalues o...
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作者：Cohen-Alloro, Omri; Peled, Ron
作者单位：Tel Aviv University
摘要：Motivated by questions on the delocalization of random surfaces, we prove that random surfaces satisfying a Lipschitz constraint rarely develop extremal gradients. Previous proofs of this fact relied on reflection positivity and were thus limited to random surfaces defined on highly symmetric graphs, whereas our argument applies to general graphs. Our proof makes use of a cluster algorithm and reflection transformation for random surfaces of the type introduced by Swendsen-Wang, Wolff and Ever...
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作者：Barnes, Clayton L.
作者单位：Technion Israel Institute of Technology
摘要：In 2001, Frank Knight constructed a stochastic process modeling the one-dimensional interaction of two particles, one being Newtonian in the sense that it obeys Newton's laws of motion, and the other particle being Brownian. We construct a multi-particle analog, using Skorohod map estimates in proving a propagation of chaos, and characterizing the hydrodynamic limit as the solution to a PDE with free boundary condition. This PDE resembles the Stefan problem but has a Neumann type boundary cond...
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作者：Podolskij, Mark; Veliyev, Bezirgen; Yoshida, Nakahiro
作者单位：Aarhus University; CREATES; Aarhus University; University of Tokyo
摘要：In this paper we present the Edgeworth expansion for the Euler approximation scheme of a continuous diffusion process driven by a Brownian motion. Our methodology is based upon a recent work (Stochastic Process. Appl. 123 (2013) 887-933), which establishes Edgeworth expansions associated with asymptotic mixed normality using elements of Malliavin calculus. Potential applications of our theoretical results include higher order expansions for weak and strong approximation errors associated to th...
