The Annals of Probability

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• Transition from the annealed to the quenched asymptotics for a random walk on random obstacles AI翻译
  作者：Ben Arous, G; Molchanov, S; Ramírez, AF
  作者单位：New York University; University of North Carolina; University of North Carolina Charlotte; Pontificia Universidad Catolica de Chile
  摘要：In this work we study a natural transition mechanism describing the passage from a quenched (almost sure) regime to an annealed (in average) one, for a symmetric simple random walk on random obstacles on sites having an identical and independent law. The transition mechanism we study was first proposed in the context of sums of identical independent random exponents by Ben Arous, Bogachev and Molchanov in [Probab. Theory Related Fields 132 (2005) 579-612]. Let p(x, t) be the survival probabili...
• Concentration around the mean for maxima of empirical processes AI翻译
  作者：Klein, T; Rio, E
  作者单位：Universite Paris Saclay
  摘要：In this paper we give optimal constants in Talagrand's concentration inequalities for maxima of empirical processes associated to independent and eventually nonidentically distributed random variables. Our approach is based on the entropy method introduced by Ledoux.
• Asymptotic expansions for the Laplace approximations of sums of Banach space-valued random variables AI翻译
  作者：Albeverio, S; Liang, S
  作者单位：University of Bonn; Tohoku University
  摘要：Let X-i, i epsilon N, be i.i.d. B-valued randorn variables, where B is a real separable Banach space. Let Phi be a smooth enough mapping from B into R. An asymptotic evaluation of Z(n) = E(exp(nPhi(Sigma(i=1)(n) X-i/n))), up to a factor (1 + o(1)), has been gotten in Bolthausen [Probab. Theory Related Fields 72 (1986) 305-318] and Kusuoka and Liang [Probab. Theory Related Fields 16 (2000) 221-238]. In this paper, a detailed asymptotic expansion of Z(n) as n --> infinity is given, valid to all ...
• Precise asymptotics of small eigenvalues of reversible diffusions in the metastable regime AI翻译
  作者：Eckhoff, M
  作者单位：University of Zurich
  摘要：We investigate the close connection between metastability of the reversible diffusion process X defined by the stochastic differential equation dX(t) = -delF(X-t) dt + root2epsilondW(t), epsilon > 0, and the spectrum near zero of its generator -L-epsilon equivalent to epsilonDelta - delF (.) del, where F: R-d --> R and W denotes Brownian motion on R-d. For generic F to each local minimum of F there corresponds a metastable state. We prove that the distribution of its resealed relaxation time c...
• Logarithmic Sobolev inequality for zero-range dynamics AI翻译
  作者：Pra, PD; Posta, G
  作者单位：University of Padua; Polytechnic University of Milan
  摘要：We prove that the logarithmic Sobolev constant for zero-range processes in a box of diameter L grows as L-2.
• Diffusion in random environment and the renewal theorem AI翻译
  作者：Cheliotis, D
  作者单位：University of Toronto
  摘要：According to a theorem of Schumacher and Brox, 2 for a diffusion X in a Brownian environment, it holds that (X-t - b(log)t)/log(2) t -> 0 in probability, as t -> infinity, where b is a stochastic process having an explicit description and depending only on the environment. We compute the distribution of the number of sign changes for b on an interval [1, x] and study some of the consequences of the computation; in particular, we get the probability of b keeping the same sign on that interval. ...
• Barycenters of measures transported by stochastic flows AI翻译
  作者：Arnaudon, M; Li, XM
  作者单位：Universite de Poitiers; Nottingham Trent University
  摘要：We investigate the evolution of barycenters of masses transported by stochastic flows. The state spaces under consideration are smooth affine manifolds with certain convexity structure. Under suitable conditions on the flow and on the initial measure, the barycenter {Z} is shown to be a semimartingale and is described by a stochastic differential equation. For the hyperbolic space the barycenter of two independent Brownian particles is a martingale and its conditional law converges to that of ...
• On dynamical Gaussian random walks AI翻译
  作者：Khoshnevisan, D; Levin, DA; Méndez-Hernández, PJ
  作者单位：Utah System of Higher Education; University of Utah
  摘要：Motivated by the recent work of Benjamini, Haggstrom, Peres and Steif [Ann. Probab. 34 (2003) 1-34] on dynamical random walks, we do the following: (i) Prove that, after a suitable normalization, the dynamical Gaussian walk converges weakly to the Ornstein-Uhlenbeck process in classical Wiener space; (ii) derive sharp tail-asymptotics for the probabilities of large deviations of the said dynamical walk; and (iii) characterize (by way of an integral test) the minimal envelope(s) for the growth-...
• Sectorial convergence of U-statistics AI翻译
  作者：Gadidov, A
  作者单位：University System of Georgia; Kennesaw State University
  摘要：In this note we show that almost sure convergence to zero of symmetrized U-statistics indexed by a linear sector in Z(+)(d) is equivalent to convergence along the diagonal of Z(+)(d), as it is considered in Latala and Zinn [Ann. Probab. 28 (2000) 1908-1924]. Comparisons with similar results for sums of multiindexed i.i.d. random variables are also made.
• An almost sure invariance principle for the range of planar random walks AI翻译
  作者：Bass, RF; Rosen, J
  作者单位：University of Connecticut; City University of New York (CUNY) System; College of Staten Island (CUNY)
  摘要：For a symmetric random walk in Z(2) with 2 + delta moments, we represent vertical bar R(n)vertical bar, the cardinality of the range, in terms of an expansion involving the renormalized intersection local times of a Brownian motion. We show that for each k >= 1 [Graphics] where Wt is a Brownian motion, W(t)((n)) = Wnt/root n, gamma j,n is the renormalized intersection local time at time 1 for W((n)) and c(X) is a constant depending on the distribution of the random walk.