-
作者：Broman, EI
作者单位：Chalmers University of Technology
摘要：Given a trigonometric polynomial f : [0, 1] -> [0, 1] of degree m, one can define a corresponding stationary process {X-i}(i is an element of Z) via determinants of the Toeplitz matrix for f. We show that for m = 1 this process, which is trivially one-dependent, is a two-block-factor.
-
作者：Balan, RM
作者单位：University of Ottawa
摘要：In this paper we generalize Yu's [Ann. Probab. 24 (1996) 2079-2097] strong invariance principle for associated sequences to the multi-parameter case, under the assumption that the covariance coefficient u(n) decays exponentially as n -> infinity. The main tools that we use are the following: the Berkes and Morrow [Z. Wahrsch. Verw. Gebiete 57 (1981) 15-37] multiparameter blocking technique, the Csorgo and Revesz [Z. Wahrsch. Verw.. Gebiete 31 (1975) 255-260] quantile transform method and the B...
-
作者：Dzhaparidze, K; van Zanten, H
作者单位：Vrije Universiteit Amsterdam
摘要：In this paper we develop the spectral theory of the fractional Brownian motion (fBm) using the ideas of Krein's work on continuous analogous of orthogonal polynomials on the unit circle. We exhibit the functions which are orthogonal with respect to the spectral measure of the fBm and obtain an explicit reproducing kernel in the frequency domain. We use these results to derive an extension of the classical Paley-Wiener expansion of the ordinary Brownian motion to the fractional case.
-
作者：Csiszár, I; Matús, F
作者单位：Hungarian Academy of Sciences; Czech Academy of Sciences; Institute of Information Theory & Automation of the Czech Academy of Sciences
摘要：The variation distance closure of an exponential family with a convex set of canonical parameters is described, assuming no regularity conditions. The tools are the concepts of convex core of a measure and extension of an exponential family, introduced previously by the authors, and a new concept of accessible faces of a convex set. Two other closures related to the information divergence are also characterized.
-
作者：Seppäläinen, T
作者单位：University of Wisconsin System; University of Wisconsin Madison
摘要：Fluctuations from a hydrodynamic limit of a one-dimensional asymmetric system come at two levels. On the central limit scale n (1/2) one sees initial fluctuations transported along characteristics and no dynamical noise. The second order of fluctuations comes from the particle current across the characteristic. For a system made up of independent random walks we show that the second-order fluctuations appear at scale n (1/4) and converge to a certain self-similar Gaussian process. If the syste...
-
作者：Boucheron, S; Bousquet, O; Lugosi, G; Massart, P
作者单位：Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); Max Planck Society; Pompeu Fabra University; Universite Paris Saclay
摘要：A general method for obtaining moment inequalities for functions of independent random variables is presented. It is a generalization of the entropy method which has been used to derive concentration inequalities for such functions [Boucheron, Lugosi and Massart Anti. Probab. 31 (2003) 1583-1614], and is based on a generalized tensorization inequality due to Latala and Oleszkiewicz [Lecture Notes in Math. 1745 (2000) 147-168]. The new inequalities prove to be a versatile tool in a wide range o...
-
作者：Afanasyev, VI; Geiger, J; Kersting, G; Vatutin, VA
作者单位：Russian Academy of Sciences; Steklov Mathematical Institute of the Russian Academy of Sciences; Goethe University Frankfurt; University of Kaiserslautern
摘要：We study branching processes in an i.i.d. random environment, where the associated random walk is of the oscillating type. This class of processes generalizes the classical notion of criticality. The main properties of such branching processes are developed under a general assumption, known as Spitzer's condition in fluctuation theory of random walks, and some additional moment condition. We determine the exact asymptotic behavior of the survival probability and prove conditional functional li...
-
作者：Kupsa, M; Lacroix, Y
作者单位：Charles University Prague; Universite de Toulon
摘要：In this paper we characterize possible asymptotics for hitting times in aperiodic ergodic dynamical systems: asymptotics are proved to be the distribution functions of subprobability measures on the line belonging to the functional class [GRAPHICS] Note that all possible asymptotics are absolutely continuous.
-
作者：Tindel, S
作者单位：Universite de Lorraine
摘要：In this note we show how to generalize the stochastic calculus method introduced by Comets and Neveu [Comm. Math. Phys. 166 (1995) 549-564] for two models of spin glasses, namely, the SK model with external field and the perceptron model. This method allows to derive quite easily some fluctuation results for the free energy in those two cases.
-
作者：Piau, D
作者单位：Universite Claude Bernard Lyon 1
摘要：We extend in two directions our previous results about the sampling and the empirical measures of immortal branching Markov processes. Direct applications to molecular biology are rigorous estimates of the mutation rates of polymerase chain reactions from uniform samples of the population after the reaction. First, we consider nonhomogeneous processes, which are more adapted to real reactions. Second, recalling that the first moment estimator is analytically known only in the infinite populati...
