-
作者：Li, XD
作者单位：University of Oxford; Universite de Toulouse; Universite Toulouse III - Paul Sabatier
摘要：We first prove the LP-convergence (p greater than or equal to 1) and a Fernique-type exponential integrability of divergence functionals for all Cameron-Martin vector fields with respect to the pinned Wiener measure on loop spaces over a compact Riemannian manifold. We then prove that the Driver flow is a smooth transform on path spaces in the sense of the Malliavin calculus and has an infinity-quasi-continuous modification which can be quasi-surely well defined on path spaces. This leads us t...
-
作者：Hall, P; Wang, QY
作者单位：Australian National University; University of Sydney
摘要：The leading term in the normal approximation to the distribution of Student's t statistic is derived in a general setting, with the sole assumption being that the sampled distribution is in the domain of attraction of a normal law. The form of the leading term is shown to have its origin in the way in which extreme data influence properties of the Studentized sum. The leading-term approximation is used to give the exact rate of convergence in the central limit theorem up to order n(-1/2), wher...
-
作者：Chen, LHY; Xia, AH
作者单位：National University of Singapore; University of Melbourne
摘要：The framework of Stein's method for Poisson process approximation is presented from the point of view of Palm theory, which is used to construct Stein identities and define local dependence. A general result (Theorem 2.3) in Poisson process approximation is proved by taking the local approach. It is obtained without reference to any particular metric, thereby allowing wider applicability. A Wasserstein pseudometric is introduced for measuring the accuracy of point process approximation. The ps...
-
作者：Tarrés, P
作者单位：Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Centre National de la Recherche Scientifique (CNRS); University of Neuchatel
摘要：Vertex-reinforced random walk (VRRW), defined by Pemantle in 1988, is a random process that takes values in the vertex set of a graph G, which is more likely to visit vertices it has visited before. Pemantle and Volkov considered the case when the underlying graph is the one-dimensional integer lattice Z. They proved that the range is almost surely finite and that with positive probability the range contains exactly five points. They conjectured that this second event holds with probability 1....
-
作者：Chang, CC; Landim, C; Lee, TY
作者单位：National Taiwan University; Universite de Rouen Normandie; Centre National de la Recherche Scientifique (CNRS)
摘要：We prove a large deviations principle for the occupation time of a site in the two-dimensional symmetric simple exclusion process. The decay probability rate is of order t/logt and the rate function is given by Y-alpha(beta) = (pi/2){sin(-1)(2beta - 1) - sin(-1) (2alpha - 1))(2). The proof relies on a large deviations principle for the polar empirical measure which contains an interesting log scale spatial average. A contraction principle permits us to deduce the occupation time large deviatio...
-
作者：Hsing, T; Wu, WB
作者单位：Texas A&M University System; Texas A&M University College Station; University of Chicago
摘要：A weighted U-statistic based on a random sample X-1,..., X-n has the form U-n = Sigma(1less than or equal toi, jless than or equal ton) w(i-j) K(X-i, X-j), where K is a fixed symmetric measurable function and the w(i) are symmetric weights. A large class of statistics can be expressed as weighted U-statistics or variations thereof. This paper establishes the asymptotic normality of U-n when the sample observations come from a nonlinear time series and linear processes.
-
作者：Attal, SP; Lindsay, JM
作者单位：Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); University of Nottingham
摘要：Quantum stochastic calculus is extended in a new formulation in which its stochastic integrals achieve their natural and maximal domains. Operator adaptedness, conditional expectations and stochastic integrals are all defined simply in terms of the orthogonal projections of the time filtration of Fock space, together with sections of the adapted gradient operator. Free from exponential vector domains, our stochastic integrals may be satisfactorily composed yielding quantum Ito formulas for ope...
-
作者：Dalang, RC; Lévêque, O
作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
摘要：We study a class of linear hyperbolic stochastic partial differential equations in bounded domains, which includes the wave equation and the telegraph equation, driven by Gaussian noise that is white in time but not in space. We give necessary and sufficient conditions on the spatial correlation of the noise for the existence (and uniqueness) of square-integrable solutions. In the particular case where the domain is a ball and the noise is concentrated on a sphere, we characterize the isotropi...
-
作者：Mathieu, P; Remy, E
作者单位：Aix-Marseille Universite
摘要：We prove that the heat kernel on the infinite Bernoulli percolation cluster in Z(d) almost surely decays faster than t(-d/2). We also derive estimates on the mixing time for the random walk confined to a finite box. Our approach is based on local isoperimetric inequalities. Some of the results of this paper were previously announced in the note of Mathieu and Remy.
-
作者：Kösters, H
作者单位：University of Munster
摘要：Let X-1, X-2,... be a sequence of [0, 1]-valued i.i.d. random variables, let c greater than or equal to 0 be a sampling cost for each observation and let Y-i = X-i - ic, i = 1, 2,.... For n = 1, 2,..., let M(Y-1,..., Y-n) = E(max(1 less than or equal to i) (less than or equal to n) Y-i) and V(Y-1,..., Y-n) sup(tauis an element ofC)(n) E(Y-tau), where C-n denotes the set of all stopping rules for Y-1,..., Y-n. Sharp upper bounds for the difference M(Y-1,..., Y-n) -V (Y-1,..., Y-n) are given und...
