2005

最新文章

• Rescaled Lotka-Volterra models converge to super-Brownian motion AI翻译
  作者：Cox, JT; Perkins, EA
  作者单位：Syracuse University; University of British Columbia
  摘要：We show that a sequence of stochastic spatial Lotka-Volterra models, suitably rescaled in space and time, converges weakly to super-Brownian motion with drift. The result includes both long range and nearest neighbor models, the latter for dimensions three and above. These theorems are special cases of a general convergence theorem for perturbations of the voter model.
• A new maximal inequality and invariance principle for stationary sequences AI翻译
  作者：Peligrad, M; Utev, S
  作者单位：University System of Ohio; University of Cincinnati; University of Nottingham
  摘要：We derive a new maximal inequality for stationary sequences under a martingale-type condition introduced by Maxwell and Woodroofe [Ann. Probab. 28 (2000) 713-724]. Then, we apply it to establish the Donsker invariance principle for this class of stationary sequences. A Markov chain example is given in order to show the optimality of the conditions imposed.
• Central limit theorems for sequences of multiple stochastic integrals AI翻译
  作者：Nualart, D; Peccati, G
  作者单位：University of Barcelona; Sorbonne Universite
  摘要：We characterize the convergence in distribution to a standard normal law for a sequence of multiple stochastic integrals of a fixed order with variance converging to 1. Some applications are given, in particular to study the limiting behavior of quadratic functionals of Gaussian processes.
• 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 ...