The Annals of Probability

最新文章

• Second class particles and cube root asymptotics for Hammersley's process AI翻译
  作者：Cator, Eric; Groeneboom, Piet
  作者单位：Delft University of Technology; Vrije Universiteit Amsterdam
  摘要：We show that, for a stationary version of Hammersley's process, with Poisson sources on the positive x-axis and Poisson sinks on the positive y-axis, the variance of the length of a longest weakly North-East path L(t, t) from (0, 0) to (t, t) is equal to 2E(t - X(t))+, where X(t) is the location of a second class particle at time t. This implies that both E(t - X(t))+ and the variance of L (t, t) are of order t(2/3). Proofs are based on the relation between the flux and the path of a second cl...
• Maxima of asymptotically Gaussian random fields and moderate deviation approximations to boundary crossing probabilities of sums of random variables with multidimensional indices AI翻译
  作者：Chan, HP; Lai, TL
  作者单位：National University of Singapore; Stanford University
  摘要：Several classical results on boundary crossing probabilities of Brownian motion and random walks are extended to asymptotically Gaussian random fields, which include sums of i.i.d. random variables with multidimensional indices, multivariate empirical processes, and scan statistics in change-point and signal detection as special cases. Some key ingredients in these extensions are moderate deviation approximations to marginal tail probabilities and weak convergence of the conditional distributi...
• Bulk diffusion in a system with site disorder AI翻译
  作者：Quastel, Jeremy
  作者单位：University of Toronto
  摘要：We consider a system of random walks in a random environment interacting via exclusion. The model is reversible with respect to a family of disordered Bernoulli measures. Assuming some weak mixing conditions, it is shown that, under diffusive scaling, the system has a deterministic hydrodynamic limit which holds for almost every realization of the environment. The limit is a nonlinear diffusion equation with diffusion coefficient given by a variational formula. The model is nongradient and the...
• Poincare and transportation inequalities for Gibbs measures under the Dobrushin uniqueness condition AI翻译
  作者：Wu, Liming
  作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Clermont Auvergne (UCA); Wuhan University
  摘要：In in this paper we establish an explicit and sharp estimate of the spectral gap (Poincare inequality) and the transportation inequality for Gibbs measures, under the Dobrushin uniqueness condition. Moreover, we give a generalization of the Liggett's M - epsilon theorem for interacting particle systems.
• A Gaussian kinematic formula AI翻译
  作者：Taylor, JE
  作者单位：Stanford University
  摘要：In this paper we consider probabilistic analogues of some classical integral geometric formulae: Weyl-Steiner tube formulae and the Chern-Federer kinematic fundamental formula. The probabilistic building blocks are smooth, real-valued random fields built up from i.i.d. copies of centered, unit-variance smooth Gaussian fields on a manifold M. Specifically, we consider random fields of the form f(p) = F(y(1) (p),..., y(k) (p)) for F is an element of C-2 (R-k ; R) and (y(1),..., y(k)) a vector of...
• A theorem on majorizing measures AI翻译
  作者：Bednorz, Witold
  作者单位：University of Warsaw
  摘要：Let (T,d) be a metric space and phi:R+ -> R an increasing, convex function with phi(0) = 0. We prove that if m is a probability measure m on T which is majorizing with respect to d, phi, that is, delta := sup(x epsilon T)integral(D(T))(0)phi(-1)(1/m(B(x, epsilon))) d epsilon < infinity, then E sup(s,t epsilon T)vertical bar X(s)-X(t)vertical bar <= 32 delta for each separable stochastic process X(t), t epsilon T, which satisfies E phi vertical bar X(s) - X(t)vertical bar/d(s,t) <= 1 for all s,...
• Spectral gap for the zero range process with constant rate AI翻译
  作者：Morris, Ben
  作者单位：University of California System; University of California Davis
  摘要：We solve an open problem concerning the relaxation time (inverse spectral gap) of the zero range process in Z(d)/LZ(d) with constant rate, proving a tight upper bound of 0 ((p + 1)(2)L(2)), where p is the density of particles.
• The Shannon information of filtrations and the additional logarithmic utility of insiders AI翻译
  作者：Ankirchner, Stefan; Dereich, Steffen; Imkeller, Peter
  作者单位：Humboldt University of Berlin; Technical University of Berlin
  摘要：The background for the general mathematical link between utility and information theory investigated in this paper is a simple financial market model with two kinds of small traders: less informed traders and insiders, whose extra information is represented by an enlargement of the other agents' filtration. The expected logarithmic utility increment, that is, the difference of the insider's and the less informed trader's expected logarithmic utility is described in terms of the information dri...
• Notes on the two-dimensional, fractional Brownian motion AI翻译
  作者：Baudoin, F; Nualart, D
  作者单位：University of Barcelona
  摘要：We study the two-dimensional fractional Brownian motion with Hurst parameter H > (1)/(2). In particular, we show, using stochastic calculus, that this process admits a skew-product decomposition and deduce from this representation some asymptotic properties of the motion.
• Finitely additive beliefs and universal type spaces AI翻译
  作者：Meier, M
  作者单位：Consejo Superior de Investigaciones Cientificas (CSIC); CSIC - Institut d'Analisi Economica (IAE)
  摘要：The probabilistic type spaces in the sense of Harsanyi [Management Sci. 14 (1967/68) 159-182, 320-334, 486-502] are the prevalent models used to describe interactive uncertainty. In this paper we examine the existence of a universal type space when beliefs are described by finitely additive probability measures. We find that in the category of all type spaces that satisfy certain measurability conditions (kappa-measurability, for some fixed regular cardinal K), there is a universal type space ...