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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...
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作者：Bryc, Wlodzimierz
作者单位：University System of Ohio; University of Cincinnati
摘要：We derive a non-asymptotic expression for the moments of traces of monomials in several independent complex Wishart matrices, extending some explicit formulas available in the literature. We then deduce the explicit expression for the cumulants. From the latter, we read out the multivariate normal approximation to the traces of finite families of polynomials in independent complex Wishart matrices.
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作者：Aidekon, Elie
作者单位：Sorbonne Universite; Universite Paris Cite
摘要：We consider a transient random walk (X-n) in random environment on a Galton-Watson tree. Under fairly general assumptions, we give a sharp and explicit criterion for the asymptotic speed to be positive. As a consequence, situations with zero speed are revealed to occur. In such cases, we prove that X-n is of order of magnitude n(Lambda), with Lambda is an element of (0, 1). We also show that the linearly edge reinforced random walk on a regular tree always has a positive asymptotic speed, whic...
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作者：Janvresse, Elise; Rittaud, Benoit; de la Rue, Thierry
作者单位：Universite de Rouen Normandie; Centre National de la Recherche Scientifique (CNRS); Universite Paris 13
摘要：We study the random Fibonacci sequences defined by F-1 = F-2 = (F) over tilde (1) = (F) over tilde (2) = 1 and for n >= 1, Fn+2 = Fn+1 +/- F-n (linear case) and (F) over tilde (n+2) = vertical bar(F) over tilde (n+1) +/- (F) over tilde (n)vertical bar (non-linear case), where each +/- sign is independent and either + with probability p or - with probability 1 - p (0 < p <= 1). Our main result is that the exponential growth of F-n for 0 < p <= 1, and of F-n for 0 < p < <= 1, and of (F) over til...
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作者：Kargin, Vladislav
作者单位：New York University
摘要：This paper establishes necessary and sufficient conditions for the sequence of products of freely independent unitary operators to converge in distribution to the uniform law on the unit circle.
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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...
