-
作者：Klass, MJ; Nowicki, K
作者单位：University of California System; University of California Berkeley; Lund University
摘要：Let B be a Banach space and F any family of bounded linear functionals on B of norm at most one. For x is an element of B set \\X\\ = sup(Lambda is an element ofF) Lambda>(*) over bar * (x) (\\.\\ is at least a seminorm on B), We give probability estimates for the tail probability of S-n* = max(1 less than or equal tok less than or equal ton) \\Sigma (k)(j=1) X-j\\ where {X-i}(i=1)(n) are independent symmetric Banach space valued random elements. Our method is based on approximating the probab...
-
作者：Mikosch, T; Resnick, S; Samorodnitsky, G
作者单位：University of Groningen; Cornell University
摘要：We consider the maximum of the periodogram based on an infinite variance heavy-tailed sequence. For alpha < 1 we show that the maxima constitute a weakly convergent sequence and find its limiting distribution. For 1 alpha < 2 we show that the sequence of the maxima is not tight and find a normalization that makes it tight.
-
作者：Nishiyama, Y
作者单位：Research Organization of Information & Systems (ROIS); Institute of Statistical Mathematics (ISM) - Japan
摘要：This paper deals with weak convergence of stochastic integrals with respect to multivariate point processes. The results are given in terms of an entropy condition for partitioning of the index set of the integrands, which is a sort of L-2-bracketing. We also consider l(infinity)-valued martingale difference arrays, and present natural generalizations of Jain-Marcus's and Ossiander's central limit theorems. As an application, the asymptotic behavior of log-likelihood ratio random fields in gen...
-
作者：Kobylanski, M
作者单位：Universite de Tours
摘要：We provide existence, comparison and stability results for one-dimensional backward stochastic differential equations (BSDEs) when the coefficient (or generator) F(t, Y, Z) is continuous and has a quadratic growth in Z and the terminal condition is bounded. We also give, in this framework, the links between the solutions of BSDEs set on a diffusion and viscosity or Sobolev solutions of the corresponding semilinear partial differential equations.
-
作者：Deheuvels, P
作者单位：Sorbonne Universite
摘要：The notion of a kth iterated Kiefer process K(nu, t; k) for k is an element of N and nu, t is an element of R is introduced. We show that the uniform quantile process beta (n)(t) may be approximated on [0, 1] by n(-1/2) K(n, t; k), at an optimal uniform almost sure rate of O(n(-1/2+1/2k+1+0(1))) for each k is an element of N. Our arguments are based in part on a new functional limit law, of independent interest, for the increments of the empirical process; Applications include an extended vers...
-
作者：Maxwell, M; Woodroofe, M
作者单位：California State University System; San Jose State University; University of Michigan System; University of Michigan
摘要：Central limit theorems and invariance principles are obtained for additive functionals of a stationary ergodic Markov chain, say S-n = g(X-1) + ... + g(X-n), where E[g(X-1)] = 0 and E[g(X-1)(2)] < . The conditions imposed restrict the moments of g and the growth of the conditional means E(S-n\X-1). No other restrictions on the dependence structure of the chain are required. When specialized to shift processes, the conditions are implied by simple integral tests involving g.
-
作者：Hug, D; Last, G
作者单位：University of Freiburg; Helmholtz Association; Karlsruhe Institute of Technology
摘要：This paper is concerned with contact distribution functions of a random closed set Xi = U(n=1)(infinity) Xi (n) in R(d), where the Xi (n) are assumed to be random nonempty convex bodies. These distribution functions are defined here in terms of a distance function which is associated with a strictly convex gauge body (structuring element) that contains the origin in its interior. Support measures with respect to such distances will be introduced and extended to sets in the local convex ring. T...
-
作者：Zhang, TS
作者单位：University of Manchester
摘要：In this paper, we establish a small time large deviation principle and obtain the following small time asymptotics: lim(t-->0) 2t log P(X-0 is an element of B, X-t is an element of C) = -d(2)(B, C), for diffusion processes on Hilbert spaces, where d(B, C) is the intrinsic metric between two subsets B and C associated with the diffusions. The case of perturbed Ornstein-Uhlenbeck processes is treated separately at the end of the paper.
-
作者：Kenyon, R
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Saclay
摘要：Let U be a multiply connected region in R-2 with smooth boundary. Let P-epsilon be a polyomino in epsilonZ(2) approximating U as epsilon --> 0. We show that, for certain boundary conditions on P-epsilon, the height distribution on a random domino tiling (dimer covering) of P-epsilon is conformally invariant in the limit as epsilon tends to 0, in the sense that the distribution of heights of boundary components (or rather, the difference of the heights from their mean values) only depends on th...
-
作者：Massart, P
作者单位：Universite Paris Saclay
摘要：We propose some explicit values for the constants involved in the exponential concentration inequalities for empirical processes which are due to Talagrand. It has been shown by Ledoux that deviation inequalities for empirical processes could be obtained by iteration of logarithmic Sobolev type inequalities. Our approach follows closely that of Ledoux. The improvements that we get with respect to Ledoux's work are based on refinements of his entropy inequalities and computations.
