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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：Faggionato, A.; Jara, M.; Landim, C.
作者单位：Sapienza University Rome; Universite de Rouen Normandie; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：Consider a system of particles performing nearest neighbor random walks on the lattice Z under hard-core interaction. The rate for a jump over a given bond is direction-independent and the inverse of the jump rates are i.i.d. random variables belonging to the domain of attraction of an alpha-stable law, 0 < alpha < 1. This exclusion process models conduction in strongly disordered 1D media. We prove that, when varying over the disorder and for a suitable slowly varying function L, under the su...
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作者：Ambrosio, Luigi; Savare, Giuseppe; Zambotti, Lorenzo
作者单位：Universite Paris Cite; Sorbonne Universite; Scuola Normale Superiore di Pisa; University of Pavia
摘要：We study Markov processes associated with stochastic differential equations, whose non-linearities are gradients of convex functionals. We prove a general result of existence of such Markov processes and a priori estimates on the transition probabilities. The main result is the following stability property: if the associated invariant measures converge weakly, then the Markov processes converge in law. The proofs are based on the interpretation of a Fokker-Planck equation as the steepest desce...
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作者：Peche, Sandrine
作者单位：Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA)
摘要：For sample covariance matrices with i.i.d. entries with sub-Gaussian tails, when both the number of samples and the number of variables become large and the ratio approaches one, it is a well-known result of Soshnikov that the limiting distribution of the largest eigenvalue is same that of Gaussian samples. In this paper, we extend this result to two cases. The first case is when the ratio approaches an arbitrary finite value. The second case is when the ratio becomes infinite or arbitrarily s...
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作者：Khoshnevisan, Davar; Xiao, Yimin
作者单位：Utah System of Higher Education; University of Utah; Michigan State University
摘要：Let X-1 , . . . , X-N denote N independent d-dimensional Levy processes, and consider the N-parameter random field (sic)(t) := X-1(t(1))+ . . . + X-N (t(N)). First we demonstrate that for all nonrandom Borel sets F subset of R-d, the Minkowski sum (sic)(R-+(N)) circle plus F, of the range (sic)(R-+(N)) of (sic) with F, can have positive d-dimensional Lebesgue measure if and only if a certain capacity of F is positive. This improves our earlier joint effort with Yuquan Zhong by removing a certa...
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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...
