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作者：Roeckner, Michael; Zhang, Xicheng
作者单位：Huazhong University of Science & Technology; University of Bielefeld; Purdue University System; Purdue University; Purdue University System; Purdue University; University of New South Wales Sydney
摘要：In this paper, we prove the existence of a unique strong solution to a stochastic tamed 3D Navier-Stokes equation in the whole space as well as in the periodic boundary case. Then, we also study the Feller property of solutions, and prove the existence of invariant measures for the corresponding Feller semigroup in the case of periodic conditions. Moreover, in the case of periodic boundary and degenerated additive noise, using the notion of asymptotic strong Feller property proposed by Hairer ...
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作者：Goldenshluger, Alexander; Lepski, Oleg
作者单位：University of Haifa; Aix-Marseille Universite
摘要：In this paper we study the problem of adaptive estimation of a multivariate function satisfying some structural assumption. We propose a novel estimation procedure that adapts simultaneously to unknown structure and smoothness of the underlying function. The problem of structural adaptation is stated as the problem of selection from a given collection of estimators. We develop a general selection rule and establish for it global oracle inequalities under arbitrary L-p-losses. These results are...
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作者：Vatutin, Vladimir A.; Wachtel, Vitali
作者单位：Russian Academy of Sciences; Steklov Mathematical Institute of the Russian Academy of Sciences; Technical University of Munich
摘要：Let S-0 = 0, {S-n, n >= 1} be a random walk generated by a sequence of i.i.d. random variables X-1, X-2,... and let tau(-) = min{n >= 1 : S-n <= 0} and tau(+) = min{n >= 1 : S-n > 0}. Assuming that the distribution of X-1 belongs to the domain of attraction of an alpha-stable law we study the asymptotic behavior, as n -> infinity, of the local probabilities P(tau(+/-) = n) and prove the Gnedenko and Stone type conditional local limit theorems for the probabilities P(S-n is an element of [x, x ...
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作者：Nourdin, Ivan; Peccati, Giovanni
作者单位：Universite Paris Cite; Sorbonne Universite; Sorbonne Universite
摘要：We combine Malliavin calculus with Stein's method, in order to derive explicit bounds in the Gaussian and Gamma approximations of random variables in a fixed Wiener chaos of a general Gaussian process. Our approach generalizes, refines and unifies the central and non-central limit theorems for multiple Wiener-It integrals recently proved (in several papers, from 2005 to 2007) by Nourdin, Nualart, Ortiz-Latorre, Peccati and Tudor. We apply our techniques to prove Berry-Esseen bounds in the Breu...
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作者：Konakov, Valentin; Mammen, Enno
作者单位：University of Mannheim; Russian Academy of Sciences; Central Economics & Mathematics Institute RAS
摘要：We consider triangular arrays of Markov chains that converge weakly to a diffusion process. Second order Edgeworth type expansions for transition densities are proved. The paper differs from recent results in two respects. We allow nonhomogeneous diffusion limits and we treat transition densities with time lag converging to zero. Small time asymptotics are motivated by statistical applications and by resulting approximations for the joint density of diffusion values at an increasing grid of po...
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作者：van Handel, Ramon
作者单位：California Institute of Technology
摘要：This paper develops a connection between the asymptotic stability of nonlinear filters and a notion of observability. We consider a general class of hidden Markov models in continuous time with compact signal state space, and call such a model observable if no two initial measures of the signal process give rise to the same law of the observation process. We demonstrate that observability implies stability of the filter, i.e., the filtered estimates become insensitive to the initial measure at...
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作者：Popescu, Ionel
作者单位：University System of Georgia; Georgia Institute of Technology; Institute of Mathematics of the Romanian Academy
摘要：In this paper we discuss general tridiagonal matrix models which are natural extensions of the ones given in Dumitriu and Edelman (J. Math. Phys. 43(11): 5830-5847, 2002; J. Math. Phys. 47(11):5830-5847, 2006). We prove here the convergence of the distribution of the eigenvalues and compute the limiting distributions in some particular cases. We also discuss the limit of fluctuations, which, in a general context, turn out to be Gaussian. For the case of several random matrices, we prove the co...
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作者：Doering, Maik; Stannat, Wilhelm
作者单位：Technical University of Darmstadt
摘要：We prove that the Dirichlet form associated with the Wasserstein diffusion on the set of all probability measures on the unit interval, introduced in von Renesse and Sturm (Entropic measure and Wasserstein diffusion. Ann Probab, 2008) satisfies a logarithmic Sobolev inequality. This implies hypercontractivity of the associated transition semigroup. We also study functional inequalities for related diffusion processes.
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作者：Chatterjee, Sourav
作者单位：University of California System; University of California Berkeley
摘要：Linear statistics of eigenvalues in many familiar classes of random matrices are known to obey gaussian central limit theorems. The proofs of such results are usually rather difficult, involving hard computations specific to the model in question. In this article we attempt to formulate a unified technique for deriving such results via relatively soft arguments. In the process, we introduce a notion of 'second order Poincare inequalities': just as ordinary Poincare inequalities give variance b...
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作者：Armendariz, Ines; Loulakis, Michail
作者单位：Universidad de San Andres Argentina; Universidade de Sao Paulo; University of Crete
摘要：We prove a strong form of the equivalence of ensembles for the invariant measures of zero range processes conditioned to a supercritical density of particles. It is known that in this case there is a single site that accomodates a macroscopically large number of the particles in the system. We show that in the thermodynamic limit the rest of the sites have joint distribution equal to the grand canonical measure at the critical density. This improves the result of Grosskinsky, Schutz and Spohn,...
