Probability Theory and Related Fields

最新文章

• Lower bounds on the restitution error in the Hopfield model AI翻译
  作者：Loukianova, D
  摘要：This paper contains a first rigorous results at the direction of the converse to Newman's bounds [11] on the storage capacity for the Hopfield model of associative memory. Let m denote the number of stored patterns and N that of neurons, Assuming that m/N --> alpha as N --> infinity we show that for alpha > 0 the memory necessarily commits a positive fraction of errors on memorized patterns that becomes superior to some threshold value (approximately 0.05) as alpha --> infinity.
• Perturbed Brownian motions AI翻译
  作者：Perman, M; Werner, W
  作者单位：Universite PSL; Ecole Normale Superieure (ENS); Centre National de la Recherche Scientifique (CNRS)
  摘要：We study 'perturbed Brownian motions', that can be, loosely speaking, described as follows: they behave exactly as linear Brownian motion except when they hit their past maximum or/and maximum where they get an extra 'push'. We define with no restrictions on the perturbation parameters a process which has this property and show that its law is unique within a certain 'natural class' of processes. In the case where both perturbations (at the maximum and at the minimum) are self-repelling, we sh...
• One-sided local large deviation and renewal theorems in the case of infinite mean AI翻译
  作者：Doney, RA
  摘要：If {S-n, n greater than or equal to 0} is an integer-valued random walk such that S-n/a(n) converges in distribution to a stable law of index alpha is an element of (0, 1) as n --> infinity, then Gnedenko's local limit theorem provides a useful estimate for P{S-n = r} for values of r such that r/a(n) is bounded. The main point of this paper is to show that, under certain circumstances, there is another estimate which is valid when r/a(n) --> +infinity, in other words to establish a large devia...
• On a mapping approach to investigating the bootstrap accuracy AI翻译
  作者：Chen, KI; Lo, SH
  作者单位：Columbia University
  摘要：A simple mapping approach is proposed to study the bootstrap accuracy in a rather general setting. It is demonstrated that the bootstrap accuracy can be obtained through this method for a broad class of statistics to which the commonly used Edgeworth expansion approach may not be successfully applied. We then consider some examples to illustrate how this approach may be used to find the bootstrap accuracy and show the advantage of the bootstrap approximation over the Gaussian approximation. Fo...
• Logarithmic Sobolev inequality for generalized simple exclusion processes AI翻译
  作者：Yau, HT
  摘要：Let <(mu)over bar> be a probability measure on the set {0,1,...,R} for some R is an element of N and Lambda(L) a cube of width L in Z(d). Denote by mu(Lambda L)(gc) the (grand canonical) product measure on the configuration space on Lambda(L) with <(mu)over bar> as the marginal measure; here the superscript indicates the grand canonical ensemble. The canonical ensemble, denoted by mu(Lambda L,n)(c), is defined by conditioning mu(Lambda L)(gc) given the total number of particles to be n. Consid...
• Stochastic Jacobi fields and vector fields induced by varying area on path spaces AI翻译
  作者：Lyons, T; Qian, ZM
  摘要：We study two classes of vector fields on the path space over a closed manifold with a Wiener Riemannian measure. By adopting the viewpoint of Yang-Mills field theory, we study a vector field defined by varying a metric connection. We prove that the vector field obtained in this way satisfies a Jacobi field equation which is different from that of classical one by taking in account that a Brownian motion is invariant under the orthogonal group action, so that it is a geometric vector field on t...
• Uniform rates of convergence in the CLT for quadratic forms in multidimensional spaces AI翻译
  作者：Bentkus, V; Gotze, F
  摘要：Let X,X-1,X-2,... be a sequence of i.i.d. random vectors taking values in a d-dimensional real linear space R-d. Assume that EX = 0 and that X is not concentrated in a proper subspace of R-d. Let G denote a mean zero Gaussian random vector with the same covariance operator as that of X. We investigate the distributions of non-degenerate quadratic forms Q[S-N] of the normalized sums S-N = N-1/2(X-1 + ... + X-N) and show that [GRAPHICS] provided that d greater than or equal to 9 and the fourth m...
• On functions transforming a Wiener process into a semimartingale AI翻译
  作者：Chitashvili, R; Mania, M
  摘要：The description of the class of all functions f=(f(t,x), t greater than or equal to 0, x is an element of R) is given, for which the transformed process (f(t, W-t),t greater than or equal to 0) (where W is a standard Wiener process) is a semimartingale.
• Differentiable and analytic families of continuous martingales in manifolds with connection AI翻译
  作者：Arnaudon, M
  作者单位：Centre National de la Recherche Scientifique (CNRS); Universites de Strasbourg Etablissements Associes; Universite de Strasbourg
  摘要：We prove that the derivative of a differentiable family X-t(a) of continuous martingales in a manifold M is a martingale in the tangent space for the complete lift of the connection in M, provided that the derivative is bi-continuous in t and a. We consider a filtered probability space (Omega, (F-t)(0 less than or equal to t less than or equal to 1, P)) such that all the real martingales have a continuous version, and a manifold M endowed with an analytic connection and such that the complexif...
• About the Berry-Esseen theorem for weakly dependent sequences AI翻译
  作者：Rio, E
  摘要：We extend the method of Bergstrom for the rates of convergence in the central limit theorem to weakly dependent sequences. In particular, we prove that, for stationary and uniformly mixing sequences of real-valued and bounded random variables, the rate of convergence in the central limit theorem is of the order of n(-1/2) as soon as the sequence (theta(p))(p>0) of uniform mixing coefficients satisfies Sigma(p>0)p theta(p) < infinity.