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作者：Chen, Z.-Q.; Fitzsimmons, P. J.; Kuwae, K.; Zhang, T.-S.
作者单位：University of California System; University of California San Diego; University of Washington; University of Washington Seattle; Kumamoto University; University of Manchester
摘要：We present a path-space integral representation of the semigroup associated with the quadratic form obtained by a lower-order perturbation of the L-2-infinitesimal generator L of a general symmetric Markov process. An illuminating concrete example for L is Delta(D)- (-Delta)(s)(D), where D is a bounded Euclidean domain in R-d, s epsilon [ 0, 1], Delta(D) is the Laplace operator in D with zero Dirichlet boundary condition and -(-Delta)(D)(s) is the fractional Laplacian in D with zero exterior c...
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作者：Andjel, Enrique; Mountford, T. S.
作者单位：Aix-Marseille Universite; Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
摘要：We examine the long-range exclusion process introduced by Spitzer and studied by Liggett and answer some of the open questions raised by Liggett. In particular, we show the existence of equilibria corresponding to bounded dual harmonic functions and that the process can have right-discontinuous paths at strictly positive times. We also show that explosions when they occur, do so at fixed times determined by the initial configuration. Finally, we give an example for which the configuration with...
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作者：Khoshnevisan, Davar
作者单位：Utah System of Higher Education; University of Utah
摘要：Haggstrom et al. (Ann Inst H Poincare Probab Stat 33(4):497-528, 1997) have introduced a dynamical version of percolation on a graph G. When G is a tree they derived a necessary and sufficient condition for percolation to exist at some time t. In the case that G is a spherically symmetric tree (Peres and Steif in Probab Theory Relat Fields 111(1):141-165, 1998), derived a necessary and sufficient condition for percolation to exist at some time t in a given target set D. The main result of the ...
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作者：Barbe, Ph.; McCormick, W. P.
作者单位：University System of Georgia; University of Georgia; Centre National de la Recherche Scientifique (CNRS)
摘要：We establish some asymptotic expansions for infinite weighted convolutions of distributions having rapidly varying subexponential tails. Examples are presented, some showing that in order to obtain an expansion with two significant terms, one needs to have a general way to calculate higher order expansions, due to possible cancellations of terms. An algebraic methodology is employed to obtain the results.
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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：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...
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作者：Hughes, C. P.; Nikeghbali, A.; Yor, M.
作者单位：University of York - UK; University of Zurich; Universite Paris Cite; Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite; Universite Paris Cite
摘要：We prove a multidimensional extension of Selberg's central limit theorem for the logarithm of the Riemann zeta function on the critical line. The limit is a totally disordered process, whose coordinates are all independent and Gaussian.
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作者：Tearne, Oliver M.
作者单位：University of Warwick
摘要：This paper concerns comparisons between attractors for random dynamical systems and their corresponding noiseless systems. It is shown that if a random dynamical system has negative time trajectories that are transient or explode with probability one, then the random attractor cannot contain any open set. The result applies to any Polish space and when applied to autonomous stochastic differential equations with additive noise requires only a mild dissipation of the drift. Additionally, follow...
