The Annals of Probability

最新文章

• On the density of the maximum of smooth Gaussian processes AI翻译
  作者：Diebolt, J; Posse, C
  作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
  摘要：We obtain an integral formula for the density of the maximum of smooth Gaussian processes. This expression induces explicit nonasymptotic lower and upper bounds which are in general asymptotic to the density. Moreover, these bounds allow us to derive simple asymptotic formulas for the density with rate of approximation as well as accurate asymptotic bounds. In particular, in the case of stationary processes, the latter upper bound improves the well-known bound based on Rice's formula. In the c...
• Gaussian chaos and sample path properties of additive functionals of symmetric Markov processes AI翻译
  作者：Marcus, MB; Rosen, J
  作者单位：City University of New York (CUNY) System; College of Staten Island (CUNY)
  摘要：Let X be a strongly symmetric Hunt process with alpha-potential density u(alpha)(x, y). Let G(alpha)(2) = {mu\integral integral(u(alpha)(x, y))(2) d mu(x)d mu(y) < infinity} and let L(t)(mu) denote the continuous additive functional with Revuz measure mu. For a set of positive measures M subset of G(alpha)(2), subject to some additional regularity conditions, we consider families of continuous (in time) additive functionals L = {L(t)(mu), (t, mu) is an element of R(+) X M} of X and a second-or...
• Second-order regular variation and rates of convergence in extreme-value theory AI翻译
  作者：deHaan, L; Resnick, S
  作者单位：Cornell University
  摘要：Rates of convergence of the distribution of the extreme order statistic to its limit distribution are given in the uniform metric and the total variation metric. A second-order regular variation condition is imposed by supposing a von Mises type condition which allows a unified treatment. Rates are constructed from the parameters of the second-order regular variation condition. Some connections with Poisson processes are discussed.
• Diffusion approximation for the advection of particles in a strongly turbulent random environment AI翻译
  作者：Komorowski, T
  作者单位：New York University
  摘要：In this paper we prove several theorems concerning the motion of a particle in a random environment. The trajectory of a particle is the solution of the differential equation dx(t)/dt = V(x(t)), where V(x) = v + epsilon(1-alpha) F(x), 0 less than or equal to alpha < 1, v is a constant vector, F is a mean-zero fluctuation field and epsilon(1-alpha) is a parameter measuring the size of the fluctuations. We show that both in case of a motion of a single particle and of a particle system considere...
• A central limit theorem for the overlap in the Hopfield model AI翻译
  作者：Gentz, B
  摘要：We consider the Hopfield model with n neurons and an increasing number p = p(n) of randomly chosen patterns. Under the condition (p(3) log p)/n --> 0, we prove for every fixed choice of overlap parameters a central limit theorem as n --> infinity, which holds for almost all realizations of the random patterns. in the special case where the temperature is above the critical one and there is no external magnetic field, the condition (p(2) log p)/n --> 0 suffices. As in the case of a finite numbe...
• Random walks on the lamplighter group AI翻译
  作者：Lyons, R; Pemantle, R; Peres, Y
  作者单位：University of Wisconsin System; University of Wisconsin Madison; University of California System; University of California Berkeley
  摘要：Kaimanovich and Vershik described certain finitely generated groups of exponential growth such that simple random walk on their Cayley graph escapes from the identity at a sublinear rate, or equivalently, all bounded harmonic functions on the Cayley graph are constant. Here we focus on a key example, called G(1) by Kaimanovich and Vershik, and show that inward-biased random walks on G(1) move outward faster than simple random walk. Indeed, they escape from the identity at a linear rate provide...
• Weak convergence for weighted empirical processes of dependent sequences AI翻译
  作者：Shao, QM; Yu, H
  作者单位：Western University (University of Western Ontario)
  摘要：In this paper we establish weak convergence theorems for weighted empirical processes of strong mixing, rho-mixing and associated sequences. We apply these results to obtain Freak convergence of integral functionals of empirical processes and of mean residual life processes in reliability theory. To carry out the proofs, we develop two Rosenthal-type inequalities for strong mixing and associated sequences.
• Decreasing sequences of sigma-fields and a measure change for Brownian motion AI翻译
  作者：Dubins, L; Feldman, J; Smorodinsky, M; Tsirelson, B
  作者单位：Tel Aviv University
  摘要：Let (f(t))t(greater than or equal to 0) be the filtration of a Brownian motion (B(t))t(greater than or equal to 0) on (Omega,f,P). An example is given of a measure Q similar to P (in the sense of absolute continuity) for which (f(t))(t greater than or equal to 0) is not the filtration of any Brownian motion on (Omega,f,Q). This settles a 15-year-old question.
• Geodesics in two-dimensional first-passage percolation AI翻译
  作者：Licea, C; Newman, CM
  作者单位：New York University
  摘要：We consider standard first-passage percolation on Z(2). Geodesics are nearest-neighbor paths in Z(2), each of whose segments is time-minimizing. We prove part of the conjecture that doubly infinite geodesics do not exist. Our main tool is a result of independent interest about the coalescing of semi-infinite geodesics.
• Multiple transition points for the contact process on the binary tree AI翻译
  作者：Liggett, TM
  摘要：The contact process on Z(d) is known to have only two fundamental types of behavior: survival and extinction. Recently Pemantle discovered that the phase structure for the contact process on a tree can be more complex. There are three possible types of behavior: strong survival, weak. survival and extinction. He proved that all three occur on homogeneous trees in which each vertex has d + 1 neighbors, provided that d greater than or equal to 3, but he left, open the case d = 2. Since d = 1 cor...