2002

最新文章

• Compound Poisson process approximation AI翻译
  作者：Barbour, AD; Månsson, M
  作者单位：University of Zurich; Chalmers University of Technology
  摘要：Compound Poisson processes are often useful as approximate models, when describing the occurrence of rare events. In this paper, we develop a method for showing how close such approximations are. Our approach is to use Stein's method directly, rather than by way of declumping and a marked Poisson process; this has conceptual advantages, but entails technical difficulties. Several applications are given to illustrate the procedure.
• Laws of the iterated logarithm for the range of random walks in two and three dimensions AI翻译
  作者：Bass, RF; Kumagai, T
  作者单位：University of Connecticut; Kyoto University
  摘要：Let S-n be a random walk in Z(d) and let R-n be the range of Sn. We prove an almost sure invariance principle for R-n when d = 3 and a law of the iterated logarithm for R-n when d = 2.
• Lyapunov exponents for small random perturbations of Hamiltonian systems AI翻译
  作者：Baxendale, PH; Goukasian, L
  作者单位：University of Southern California
  摘要：Consider the stochastic nonlinear oscillator equation (x) double over dot = -x - x(3) + epsilon(2)betax + epsilonsigmax(W) over dot(t) with beta < 0 and sigma not equal 0. If 4beta + sigma(2) > 0 then for small enough epsilon > 0 the system (x, (x) over dot ) is positive recurrent in R-2 \ {(0, 0)}. Now let (λ) over bar(epsilon) denote the top Lyapunov exponent for the linearization of this equation along trajectories. The main result asserts that (λ) over bar(epsilon) = epsilon(2/3)(λ) ove...
• A convergence result for critical reversible nearest particle systems AI翻译
  作者：Mountford, T
  作者单位：University of California System; University of California Los Angeles
  摘要：We consider critical reversible nearest particle systems. We assume that the associated renewal measure has large moments as well as some regularity conditions. It is shown that such processes, started from a nontrivial ergodic translation invariant distribution, converge in distribution to the upper invariant measure.
• Random walks on discrete groups of polynomial volume growth AI翻译
  作者：Alexopoulos, GK
  作者单位：Universite Paris Saclay
  摘要：Let it be a probability measure with finite support on a discrete group Gamma of polynomial volume growth. The main purpose of this paper is to study the asymptotic behavior of the convolution powers mu*(n) of mu. If mu is centered, then we prove upper and lower Gaussian estimates. We prove a central limit theorem and we give a generalization of the Berry-Esseen theorem. These results also extend to noncentered probability measures. We study the associated Riesz transform operators. The main t...
• Stability of the overshoot for Levy processes AI翻译
  作者：Doney, RA; Maller, RA
  作者单位：University of Manchester; University of Western Australia
  摘要：We give equivalences for conditions like X (T (r))/r -->1 and X (T*(r))/ r --> 1, where the convergence is in probability or almost sure, both as r --> 0 and r --> infinity, where X is a Levy process and T(r) and T*(r) are the first exit times of X out of the strip {(t, y) : t > 0,\y\ < r} and half-plane {(t, y) : t > 0, y less than or equal to r}, respectively. We also show, using a result of Kesten, that X(T*(r))/r --> 1 a.s. as r --> 0 is equivalent to X creeping across a level.
• On the high temperature phase of the Sherrington-Kirkpatrick model AI翻译
  作者：Talagrand, M
  作者单位：Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS)
  摘要：We prove the validity of the replica-symmetric solution of the Sherrington-Kirkpatrick model in a region that (probably) coincides with the region predicted by the physicists.
• General gauge and conditional gauge theorems AI翻译
  作者：Chen, ZQ; Song, RM
  作者单位：University of Washington; University of Washington Seattle; University of Illinois System; University of Illinois Urbana-Champaign
  摘要：General gauge and conditional gauge theorems are established for a large class of (not necessarily symmetric) strong Markov processes, including Brownian motions with singular drifts and symmetric stable processes. Furthermore, new classes of functions are introduced under which the general gauge and conditional gauge theorems hold. These classes are larger than the classical Kato class when the process is Brownian motion in a bounded C domain.
• Note about first order correction for the hydrodynamic limit of symmetric simple exclusion processes with speed change in dimension d ≥ 3 AI翻译
  作者：Janvresse, E
  作者单位：Universite de Rouen Normandie; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
• A pure jump Markov process associated with Smoluchowski's coagulation equation AI翻译
  作者：Deaconu, M; Fournier, N; Tanré, E
  作者单位：Universite de Lorraine
  摘要：The aim of the present paper is to construct a stochastic process, whose law is the solution of the Smoluchowski's coagulation equation. We introduce first a modified equation, dealing with the evolution of the distribution Q(t) (dx) of the mass in the system. The advantage we take on this is that we can perform an unified study for both continuous and discrete models. The integro-partial-differential equation satisfied by {Q(t)}(tgreater than or equal to0) can be interpreted as the evolution ...