The Annals of Probability

最新文章

• Characterization of stationary measures for one-dimensional exclusion processes AI翻译
  作者：Bramson, M; Liggett, TM; Mountford, T
  作者单位：University of Minnesota System; University of Minnesota Twin Cities; University of California System; University of California Los Angeles
  摘要：The product Bernoulli measures upsilon(alpha) with densities alpha, alpha is an element of [0, 1], are the extremal translation invariant stationary measures for an exclusion process on Z with irreducible random walk kernel p(.). Stationary measures that are not translation invariant are known to exist for finite range p(.) with positive mean. These measures have particle densities that tend to 1 as x --> infinity and tend to 0 as x --> infinity; the corresponding extremal measures form a onep...
• Fluctuations of the free energy in the REM and the p-spin SK models AI翻译
  作者：Bovier, A; Kurkova, I; Löwe, M
  作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; Sorbonne Universite; Radboud University Nijmegen
  摘要：We consider the random fluctuations of the free energy in the p-spin version of the Sherrington-Kirkpatrick (SK) model in the high-temperature regime. Using the martingale approach of Comets and Neveu as used in the standard SK model combined with truncation techniques inspired by a recent paper by Talagrand on the p-spin version, we prove that the random corrections to the free energy are on a scale N-(p-2)/2 only and, after proper rescaling, converge to a standard Gaussian random variable. T...
• Necessary and sufficient conditions for the conditional central limit theorem AI翻译
  作者：Dedecker, J; Merlevède, F
  作者单位：Sorbonne Universite
  摘要：Following Lindeberg's approach, we obtain a new condition for a stationary sequence of square-integrable and real-valued random variables to satisfy the central limit theorem. In the adapted case, this condition is weaker than any projective criterion derived from Gordin's theorem [Dokl. Akad. Nauk SSSR 188 (1969) 739-741] about approximating martingales. Moreover, our criterion is equivalent to the conditional central limit theorem, which implies stable convergence (in the sense of Renyi) to ...
• A few remarks on Bryc's paper on random fields with linear regressions AI翻译
  作者：Matysiak, W; Szablowski, PJ
  作者单位：Warsaw University of Technology
  摘要：The aim of this note is to reduce a number of assumptions in the recent paper of W. Bryc by showing that some of them imply the others and to give alternative, simpler proofs of some of Bryc's results.
• Ornstein-Zernike theory for the Bernoulli bond percolation on Zd AI翻译
  作者：Campanino, M; Ioffe, D
  作者单位：University of Bologna; Technion Israel Institute of Technology
  摘要：We derive a precise Ornstein-Zernike asymptotic formula for the decay of the two-point function P-p(0 <----> x) of the Bernoulli bond percolation on the integer lattice Z(d) in any dimension d greater than or equal to 2, in any direction x and for any subcritical value of p < p(c)(d).
• Maxima of partial sums indexed by geometrical structures AI翻译
  作者：Jiang, TF
  作者单位：University of Minnesota System; University of Minnesota Twin Cities
  摘要：The maxima of partial sums indexed by squares and rectangles over lattice points and random cubes are studied in this paper. For some of these problems, the dimension (d = 1, d = 2 and d greater than or equal to 3) significantly affects the limit behavior of the maxima. However, for other problems, the maxima behave almost the same as their one-dimensional counterparts. The tools for proving these results are large deviations, the Chen-Stein method, number theory and inequalities of empirical ...
• Strict positivity of the density for simple jump processes using the tools of support theorems. Application to the Kac equation without cutoff AI翻译
  作者：Fournier, N
  作者单位：Universite de Lorraine
  摘要：Consider the one-dimensional solution X = {X-t}(tis an element of[0,T]) of a possibly degenerate stochastic differential equation driven by a (non compensated) Poisson measure. We denote by M a set of deterministic integer-valued measures associated with the considered Poisson measure. For in m is an element of M, we denote by S(m) = {S-t(m)}(tis an element of[0,T]) the skeleton associated with X. We assume some regularity conditions, which allow to define a sort of derivative DSt (m) of S-t (...
• The Euler scheme with irregular coefficients AI翻译
  作者：Yan, LQ
  作者单位：University of British Columbia
  摘要：Weak convergence of the Euler scheme for stochastic differential equations is established when coefficients are discontinuous on a set of Lebesgue measure zero. The rate of convergence is presented when coefficients are Holder continuous. Monte Carlo simulations are also discussed.
• The minimum maximum of a continuous martingale with given initial and terminal laws AI翻译
  作者：Hobson, DG; Pedersen, JL
  作者单位：University of Bath; Swiss Federal Institutes of Technology Domain; ETH Zurich
  摘要：Let (M-t)(0less than or equal totless than or equal to1) be a continuous martingale with initial law M-0 similar to mu(0), and terminal law M-1 similar to mu(1), and let S = sup(0less than or equal totless than or equal to1) M-t. In this paper we prove that there exists a greatest lower bound with respect to stochastic ordering of probability measures, on the law of S. We give an explicit construction of this bound. Furthermore a martingale is constructed which attains this minimum by solving ...
• On some random walks on Z in random medium AI翻译
  作者：Brémont, J
  作者单位：Universite de Rennes
  摘要：We consider random walks on Z in a stationary random medium, defined by an ergodic dynamical system, in the case when the possible jumps arc {-L,...,-1, 0, + 1} for sonic fixed integer L. We provide a recurrence criterion expressed in terms of the sign of the maximal Liapounov exponent of a certain random matrix and give an algorithm of calculation of that exponent. Next, we characterize the existence of the absolutely continuous invariant measure for the Markov chain of the environments viewe...