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作者：Bogdan, Krzysztof; Kulczycki, Tadeusz; Kwasnicki, Mateusz
作者单位：Wroclaw University of Science & Technology; Purdue University System; Purdue University
摘要：We prove a uniform boundary Harnack inequality for nonnegative harmonic functions of the fractional Laplacian on arbitrary open set D. This yields a unique representation of such functions as integrals against measures on D-c boolean OR {infinity} satisfying an integrability condition. The corresponding Martin boundary of D is a subset of the Euclidean boundary determined by an integral test.
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作者：Osekowski, Adam
作者单位：University of Warsaw
摘要：In the paper we focus on self-adjoint noncommutative martingales. We provide an extension of the notion of differential subordination, which is due to Burkholder in the commutative case. Then we show that there is a noncommutative analogue of the Burkholder method of proving martingale inequalities, which allows us to establish the weak type (1,1) inequality for differentially subordinated martingales. Moreover, a related sharp maximal weak type (1,1) inequality is proved.
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作者：Ben Efraim, L.; Lust-Piquard, F.
作者单位：Hebrew University of Jerusalem; Weizmann Institute of Science; CY Cergy Paris Universite
摘要：We prove L-p Poincare inequalities with suitable dimension free constants for functions on the discrete cube {- 1, 1}(n). As well known, such inequalities for p an even integer allow to recover an exponential inequality hence the concentration phenomenon first obtained by Bobkov and Gotze. We also get inequalities between the L-p norms of vertical bar|del f | and del(alpha) f, alpha > 0; moreover L-p spaces may be replaced by more general ones. Similar results hold true, replacing functions on...
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作者：Cattiaux, P.; Guillin, A.; Malrieu, F.
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; Universite Paris Nanterre; Universite PSL; Universite Paris-Dauphine; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Rennes
摘要：We use here a particle system to prove both a convergence result (with convergence rate) and a deviation inequality for solutions of granular media equation when the confinement potential and the interaction potential are no more uniformly convex. The proof of convergence is simpler than the one in Carrillo-McCann-Villani (Rev. Mat. Iberoamericana 19:971-1018, 2003; Arch. Rat. Mech. Anal. 179:217-263, 2006). All the results complete former results of Malrieu (Ann. Appl. Probab. 13:540-560, 200...
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作者：Kolesnikov, Alexander V.
作者单位：Scuola Normale Superiore di Pisa
摘要：Let gamma be a Gaussian measure on a Suslin space X, H be the corresponding Cameron-Martin space and {e (i) } subset of H be an orthonormal basis of H. Suppose that mu (n) = rho (n) center dot gamma is a sequence of probability measures which converges weakly to a probability measure mu = rho center dot gamma Consider a sequence of Dirichlet forms {E-n}, where E-n (f) = integral(x) parallel to del Hf parallel to(2)(H)p(n) d gamma and root p(n) epsilon W-2,W-1(gamma).We prove some sufficient co...
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作者：Akahori, Jiro; Uenishi, Chihiro; Yano, Kouji
作者单位：Kyoto University; Ritsumeikan University
摘要：In this paper a stochastic equation on compact groups in discrete negative time is studied. The diagonal group action on the extreme points of solutions is proved to be transitive by means of the coupling method. This result is applied to generalize Yor's work which is closely related to Tsirelson's stochastic differential equation and to give criteria for existence of a strong solution and for uniqueness in law.
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作者：Mayer-Wolf, E.; Zakai, M.
作者单位：Technion Israel Institute of Technology; Technion Israel Institute of Technology
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作者：Csorgo, Miklos; Kulik, Rafal
作者单位：University of Sydney; Carleton University; University of Wroclaw
摘要：In this paper we consider quantile and Bahadur-Kiefer processes for long range dependent linear sequences. These processes, unlike in previous studies, are considered on the whole interval (0, 1). As it is well-known, quantile processes can have very erratic behavior on the tails. We overcome this problem by considering these processes with appropriate weight functions. In this way we conclude strong approximations that yield some remarkable phenomena that are not shared with i.i.d. sequences,...
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作者：Csiszar, Imre; Matus, Frantisek
作者单位：Czech Academy of Sciences; Institute of Information Theory & Automation of the Czech Academy of Sciences; Hungarian Academy of Sciences; HUN-REN; HUN-REN Alfred Renyi Institute of Mathematics
摘要：For a standard full exponential family on R-d, or its canonically convex subfamily, the generalized maximum likelihood estimator is an extension of the mapping that assigns to the mean a is an element of R-d of a sample for which a maximizer nu* of a corresponding likelihood function exists, the member of the family parameterized by nu*. This extension assigns to each a is an element of R-d with the likelihood function bounded above, a member of the closure of the family in variation distance....
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作者：Li, Xiang-Dong
作者单位：Universite de Toulouse; Universite Toulouse III - Paul Sabatier
摘要：Under the condition that the Bakry-Emery Ricci curvature is bounded from below, we prove a probabilistic representation formula of the Riesz transforms associated with a symmetric diffusion operator on a complete Riemannian manifold. Using the Burkholder sharp L-p-inequality for martingale transforms, we obtain an explicit and dimension-free upper bound of the L-p-norm of the Riesz transforms on such complete Riemannian manifolds for all 1 < p < infinity. In the Euclidean and the Gaussian case...
