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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...
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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：Blanca, Antonio; Gheissari, Reza; Vigoda, Eric
作者单位：University System of Georgia; Georgia Institute of Technology; New York University
摘要：The random-cluster model with parameters (p, q) is a random graph model that generalizes bond percolation (q = 1) and the Ising and Potts models (q >= 2). We study its Glauber dynamics on n x n boxes Lambda(n) of the integer lattice graph Z(2), where the model exhibits a sharp phase transition at p = p(c)(q). Unlike traditional spin systems like the Ising and Potts models, the random-cluster model has non-local interactions. Long-range interactions can be imposed as external connections in the...
