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作者：Boucheron, S; Lugosi, G; Massart, P
作者单位：Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); Pompeu Fabra University
摘要：We investigate a new methodology, worked out by Ledoux and Massart, to prove concentration-of-measure inequalities. The method is based on certain modified logarithmic Sobolev inequalities. We provide some very simple and general ready-to-use inequalities. One of these inequalities may be considered as an exponential version of the Efron-Stein inequality. The main purpose of this paper is to point out the simplicity and the generality of the approach. We show how the new method can recover man...
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作者：Van den Berg, J; Járai, AA
作者单位：Centrum Wiskunde & Informatica (CWI); University of British Columbia
摘要：We study the following problem for critical site percolation on the triangular lattice. Let A and B be sites on a horizontal line e separated by distance n. Consider, in the half-plane above e, the lowest occupied crossing R-n from the half-line left of A to the half-line right of B. We show that the probability that R-n has a site at distance smaller than m from AB is of order (log(n/m))(-1), uniformly in 1 less than or equal to m less than or equal to n/2. Much of our analysis can be carried...
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作者：Hino, M; Ramírez, JA
作者单位：Kyoto University; Cornell University
摘要：This work is involved with the short-time asymptotics of diffusion semigroups in a general setting. A generalization of Fang's version of Varadhan's formula is proven for general Dirichlet spaces that are local and conservative. The intrinsic metric appearing in the formula is characterized by pointwise distance for canonical Dirichlet spaces on loop groups.
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作者：Mytnik, L; Perkins, E
作者单位：Technion Israel Institute of Technology; University of British Columbia
摘要：This paper establishes the continuity of the density of (1 + beta)-stable super-Brownian motion (0 < beta < 1) for fixed times in d = 1, and local unboundedness of the density in all higher dimensions where it exists. We also prove local unboundedness of the density in time for a fixed spatial parameter in any dimension where the density exists, and local unboundedness of the occupation density (the local time) in the spatial parameter for dimensions d greater than or equal to 2 where the loca...
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作者：Talagrand, M
作者单位：Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); University System of Ohio; Ohio State University
摘要：Given a bounded class of functions, we introduce a combinatorial quantity (related to the idea of Vapnik-Chervonenkis classes) that is much more explicit than the Koltchinskii-Pollard entropy, but is proved to be essentially of the same order.
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作者：Pitt, LD; Robeva, RS
作者单位：University of Virginia
摘要：Let Phi = {phi(x):x is an element of R-2} be a Gaussian random field on the plane. For A subset of R-2, we investigate the relationship between the sigma-field F(Phi, A) = sigma{phi(x):x is an element of A} and the infinitesimal or germ sigma-field boolean AND(epsilon>0) F(Phi, A(epsilon)), where A(epsilon) is an epsilon-neighborhood of A. General analytic conditions are developed giving necessary and sufficient conditions for the equality of these two sigma-fields. These conditions are potent...
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作者：Hsu, EP
作者单位：Northwestern University
摘要：We discuss angular convergence of Riemannian Brownian motion on a Cartan-Hadamard manifold and show that the Dirichlet problem at infinity for such a manifold is uniquely solvable under the curvature conditions -Ce(2-eta)ar(x) less than or equal to K-M(x) less than or equal to -a(2) (eta > 0) and -Cr(x)(2beta) less than or equal to K-M(x) less than or equal to -alpha(alpha - 1)/r(x)(2) (alpha > beta + 2 > 2), respectively.
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作者：Soner, HM; Touzi, N
作者单位：Koc University; Institut Polytechnique de Paris; ENSAE Paris
摘要：A smooth solution {Gamma(t)}(tis an element of[0,T]) subset of R-d of a parabolic geometric flow is characterized as the reachability set of a stochastic target problem. In this control problem the controller tries to steer the state process into a given deterministic set T with probability one. The reachability set, V(t), for the target problem is the set of all initial data x from which the state process X-X(v)(t) is an element of T for some control process v. This representation is proved b...
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作者：Stannat, W
作者单位：University of Bielefeld
摘要：We study the global properties of transition semigroups (p(t)(nu,Psi,A)) of (A, Psi)-superprocesses over compact type spaces with possibly nonzero immigration nu in various function spaces. In particular, we compare the different rates of convergence of (p(t)(nu,Psi,A)) to equilibrium. Our analysis is based on an explicit formula for the Gateaux derivative of p(t)(nu,Psi,A) F.
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作者：Gao, F; Hannig, J; Torcaso, F
作者单位：University of Idaho; Colorado State University System; Colorado State University Fort Collins; Johns Hopkins University
摘要：We will introduce a class of m-times integrated Brownian motions. The exact asymptotic expansions for the L-2-small ball probabilities will be discussed for members of this class, of which the usual m-times integrated Brownian motion is an example. Another example will be what we call an Euler-integrated Brownian motion. We will also find very sharp estimates for the asymptotics of the eigenvalues of the covariance operator of integrated Brownian motions and will, therefore, obtain exact, not ...
