Probability Theory and Related Fields

最新文章

• Boundary trace of reflecting Brownian motions AI翻译
  作者：Benjamini, I; Chen, ZQ; Rohde, S
  作者单位：Weizmann Institute of Science; University of Washington; University of Washington Seattle
  摘要：We establish a uniform dimensional result for normally reflected Brownian motion (RBM) in a large class of non-smooth domains. Hausdorff dimensions for the boundary occupation time and the boundary trace of RBM are determined. Extensions to stable-like jump processes and to symmetric reflecting diffusions are also given.
• Asymptotic analysis via Mellin transforms for small deviations in L2-norm of integrated Brownian sheets AI翻译
  作者：Fill, JA; Torcaso, F
  作者单位：Johns Hopkins University
  摘要：We use Mellin transforms to compute a full asymptotic expansion for the tail of the Laplace transform of the squared L-2-norm of any multiply-integrated Brownian sheet. Through reversion we obtain corresponding strong small-deviation estimates.
• Estimates for distances between first exit times via parabolic equations in unbounded cylinders AI翻译
  作者：Dokuchaev, N
  作者单位：University of Limerick
  摘要：First exit times and their dependence on variations of parameters are studied for diffusion processes with non-stationary coefficients. Estimates of L-p-distances and some other distances between two exit times are obtained. These estimates are based on some new prior estimates for solutions of parabolic Kolmogorov's equations with infinite horizon without Cauchy conditions.
• Random perturbations of dynamical systems and diffusion processes with conservation laws AI翻译
  作者：Freidlin, M; Weber, M
  作者单位：University System of Maryland; University of Maryland College Park
  摘要：In this paper we consider random perturbations of dynamical systems and diffusion processes with a first integral. We calculate, under some assumptions, the limiting behavior of the slow component of the perturbed system in an appropriate time scale for a general class of perturbations. The phase space of the slow motion is a graph defined by the first integral. This is a natural generalization of the results concerning random perturbations of Hamiltonian systems. Considering diffusion process...
• Monge's problem with a quadratic cost by the zero-noise limit of h-path processes AI翻译
  作者：Mikami, T
  作者单位：Hokkaido University
  摘要：We study the asymptotic behavior, in the zero-noise limit, of solutions to Schrodinger's functional equations and that of h-path processes, and give a new proof of the existence of the minimizer of Monge's problem with a quadratic cost.
• Random planar lattices and integrated superBrownian excursion AI翻译
  作者：Chassaing, P; Schaeffer, G
  作者单位：Universite de Lorraine; Institut Polytechnique de Paris; Ecole Polytechnique; Centre National de la Recherche Scientifique (CNRS)
  摘要：In this paper, a surprising connection is described between a specific brand of random lattices, namely planar quadrangulations, and Aldous' Integrated SuperBrownian Excursion (ISE). As a consequence, the radius r(n) of a random quadrangulation with n faces is shown to converge, up to scaling, to the width r = R - L of the support of the one-dimensional ISE, or precisely: n(-1/4)r(n) (law)--> (8/9)(1/4)r. More generally the distribution of distances to a random vertex in a random quadrangulati...
• Pinning class of the Wiener measure by a functional: related martingales and invariance properties AI翻译
  作者：Baudoin, F; Thieullen, M
  作者单位：Technische Universitat Wien; Universite Paris Cite; Sorbonne Universite
  摘要：For a given functional Y on the path space, we define the pinning class of the Wiener measure as the class of probabilities which admit the same conditioning given Y as the Wiener measure. Using stochastic analysis and the theory of initial enlargement of filtration, we study the transformations (not necessarily adapted) which preserve this class. We prove, in this non Markov setting, a stochastic Newton equation and a stochastic Noether theorem. We conclude the paper with some non canonical r...
• Construction of immigration superprocesses with dependent spatial motion from one-dimensional excursions AI翻译
  作者：Dawson, DA; Li, ZH
  作者单位：Carleton University; Beijing Normal University
  摘要：A superprocess with dependent spatial motion and interactive immigration is constructed as the pathwise unique solution of a stochastic integral equation carried by a stochastic flow and driven by Poisson processes of one-dimensional excursions.
• Approximation of the effective conductivity of ergodic media by periodization AI翻译
  作者：Owhadi, H
  作者单位：Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS)
  摘要：This paper is concerned with the approximation of the effective conductivity sigma (A, mu) associated to an elliptic operator del(x)A (x, eta)del(x) where for x is an element of R-d, d greater than or equal to 1, A (x, eta) is a bounded elliptic random symmetric d x d matrix and eta takes value in an ergodic probability space (X, mu). Writing A(N) (x, eta) the periodization of A(x, eta) the torus T-N(d) of dimension d and side N we prove that for mu-almost all eta lim sigma(A(N), eta) = sigma(...
• On the efficiency of selection criteria in spline regression AI翻译
  作者：Kou, SC
  作者单位：Harvard University
  摘要：This paper concerns the cubic smoothing spline approach to nonparametric regression. After first deriving sharp asymptotic formulas for the eigenvalues of the smoothing matrix, the paper uses these formulas to investigate the efficiency of different selection criteria for choosing the smoothing parameter. Special attention is paid to the generalized maximum likelihood (GML), C-P and extended exponential (EE) criteria and their marginal Bayesian interpretation. It is shown that (a) when the Bay...