2002

最新文章

• 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...
• Levy area of Wiener processes in Banach spaces AI翻译
  作者：Ledoux, M; Lyons, T; Qian, Z
  作者单位：Centre National de la Recherche Scientifique (CNRS); Universite de Toulouse; Universite Toulouse III - Paul Sabatier; University of Oxford
  摘要：The goal of this paper is to construct canonical Levy area processes for Banach space valued Brownian motions via dyadic approximations. The significance of the existence of canonical Levy area processes is that a (stochastic) integration theory can be established for such Brownian motions (in Banach spaces). Existence of flows for stochastic differential equations with infinite dimensional noise then follows via the results of Lyons and Lyons and Qian [see, e.g., System Control and Rough Path...
• On the nonuniqueness of the invariant probability for i.i.d. random logistic maps AI翻译
  作者：Athreya, KB; Dai, JJ
  作者单位：Iowa State University
  摘要：Let {X-n}(0)(infinity) be a Markov chain with values in [0, 1] generated by the iteration of random logistic maps defined by Xn+1 = f(Cn+1) (X-n) equivalent to Cn+1 X-n (1 - X-n), n = 0, 1, 2,..., with {C-n}(1)(infinity) being independent and identically distributed random variables with values in [0, 4] and independent of X-0. This paper provides a class of examples where C-i take only two values lambda and mu such that there exist two distinct invariant probability distributions pi(0) and pi...
• Gaussian limit for determinantal random point fields AI翻译
  作者：Soshnikov, A
  作者单位：University of California System; University of California Davis
  摘要：We prove that, under fairly general conditions, a properly rescaled determinantal random point field converges to a generalized Gaussian random process.
• Regularity of quasi-stationary measures for simple exclusion in dimension d ≥ 5 AI翻译
  作者：Asselah, A; Ferrari, PA
  作者单位：Aix-Marseille Universite; Universidade de Sao Paulo
  摘要：We consider the symmetric simple exclusion process on Z(d) for d greater than or equal to 5, and study the regularity of the quasi-stationary measures of the dynamics conditioned on not occupying the origin. For each rho is an element of]0, 1[, we establish uniqueness of the density of quasi-stationary measures in L-2(d(upsilonrho)), where upsilon(rho) is the stationary measure of density p. This, in turn, permits us to obtain sharp estimates for P-upsilonrho(tau > t), where tau is the first t...
• Concentration inequalities, large and moderate deviations for self-normalized empirical processes AI翻译
  作者：Bercu, B; Gassiat, E; Rio, E
  作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
  摘要：We consider the supremum W-n of self-normalized empirical processes indexed by unbounded classes of functions F. Such variables are of interest in various statistical applications, for example, the likelihood ratio tests of contamination. Using the Herbst method, we prove an exponential concentration inequality for W-n under a second moment assumption on the envelope function of F. This inequality is applied to obtain moderate deviations for W-n. We also provide large deviations results for so...
• Explicit isoperimetric constants and phase transitions in the random-cluster model AI翻译
  作者：Häggström, O; Jonasson, J; Lyons, R
  作者单位：University of Gothenburg; Indiana University System; Indiana University Bloomington; Chalmers University of Technology
  摘要：The random-cluster model is a dependent percolation model that has applications in the study of Ising and Potts models. In this paper, several new results are obtained for the random-cluster model on nonamenable graphs with cluster parameter q greater than or equal to 1. Among these, the main ones are the absence of percolation for the free random-cluster measure at the critical value and examples of planar regular graphs with regular dual where p(c)(free)(q) > p(u)(wired)(q) for q large enoug...
• On the distribution of the square integral of the Brownian bridge AI翻译
  作者：Tolmatz, L
  摘要：Smirnov obtained the distribution F for his omega(2)-test in the form of a certain series. F is identical to the distribution of the the Brownian bridge in the L-2 norm. Smirnov, Kac and Shepp determined the Laplace-Stieltjes transform of F. Anderson and Darling expressed F in terms of Bessel functions. In the present paper we compute the moments of F and their asymptotics, obtain expansions of F and its density f in terms of the parabolic cylinder functions and Laguerre functions, and determi...