1997

最新文章

• Approximation of partial sums of arbitrary iid random variables and the precision of the usual exponential upper bound AI翻译
  作者：Hahn, MG; Klass, MJ
  作者单位：Tufts University; University of California System; University of California Berkeley
  摘要：This paper quantifies the degree to which exponential bounds can be used to approximate tail probabilities of partial sums of arbitrary lid. random variables. The introduction of a single truncation allows the usual exponential upper bound to apply usefully whenever the summands are arbitrary lid. random variables. More specifically, let n be a fixed natural number and let Z, Z(1), Z(2),..., Z(n) be arbitrary i.i.d. random variables We construct a function F-Z,F- n(a), derived from the probabi...
• On the lower tail probabilities of some random series AI翻译
  作者：Lifshits, MA
  作者单位：Universites de Strasbourg Etablissements Associes; Universite de Strasbourg
  摘要：The behavior of tail probabilities P{S less than or equal to r}, r --> 0 is investigated, where S is a series S = Sigma lambda(j)Z(j) generated by some sequence of positive numbers {lambda(j)} and by a sequence {Z(j)} of independent copies of a positive random variable Z. We present the exact asymptotic expression for P{S less than or equal to r} by means of Laplace transform Lambda(gamma) = E exp{-gamma S} under weak assumptions on the behavior of the tail probabilities of Z in the vicinity o...
• Quantum operators in classical probability theory: IV. Quasi-duality and thinnings of interacting particle systems AI翻译
  作者：Sudbury, A; Lloyd, P
  作者单位：Monash University; Monash University
  摘要：Duality has proved to be a powerful technique in the study of interacting particle systems (IPS). This concept can be enlarged and a quasi-duality defined between various pairs of IPS previously thought unrelated. Consequently, theorems of a similar style to those involving duality can be deduced. The concept of quasi-duality follows naturally from our previous studies into the use of single-site operators (an idea borrowed from quantum physics) in paper II of this series. It is shown that a n...
• The mean velocity of a Brownian motion in a random Levy potential AI翻译
  作者：Carmona, P
  作者单位：Universite de Toulouse; Universite Toulouse III - Paul Sabatier
  摘要：Brownian motion in a random Levy potential V is the informal solution of the stochastic differential equation dX(t) = dB(t) - 1/2V' (X-t) dt, where B is a Brownian motion independent of V. We generalize some results of Kawazu-Tanaka, who considered for V a Brownian motion with drift, by proving that X-t/t converges almost surely to a constant, the mean velocity, which we compute in terms of the Levy exponent phi of V, defined by E[e(mV(t))] = e(-t phi(m)).
• Strong laws for local quantile processes AI翻译
  作者：Deheuvels, P
  作者单位：Sorbonne Universite
  摘要：We show that increments of size h(n) from the uniform quantile and uniform empirical processes in the neighborhood of a fixed point t(0) is an element of (0, 1) may have different rates of almost sure convergence to 0 in the range where h(n) --> 0 and nh(n)/log n --> infinity. In particular, when h(n) + n(-lambda) with 0 < lambda < 1, we obtain that these rates are identical for 1/2 < lambda < 1, and distinct for 0 < lambda < 1/2. This phenomenon is shown to be a consequence of functional laws...
• Symmetric Langevin spin glass dynamics AI翻译
  作者：Ben Arous, G; Guionnet, A
  作者单位：Universite PSL; Ecole Normale Superieure (ENS); Universite Paris Saclay
  摘要：We study the asymptotic behavior of symmetric spin glass dynamics in the Sherrington-Kirkpatrick model as proposed by Sompolinsky-Zippelius. We prove that the averaged law of the empirical measure on the path space of these dynamics satisfies a large deviation upper bound in the high temperature regime. We study the rate function which governs this large deviation upper bound and prove that it achieves its minimum value at a unique probability measure Q which is not Markovian: We deduce an ave...
• A constructive mixing condition for 2-D Gibbs measures with random interactions AI翻译
  作者：van den Berg, J
  作者单位：Centrum Wiskunde & Informatica (CWI)
  摘要：For spin systems with random, finite-range interactions, we define an analog of the usual weak mixing property, which we call weak mixing in expectation (WME). This property implies (almost sure) uniqueness of the Gibbs measure. We concentrate on the two-dimensional case, for which we present finite-volume conditions which are sufficient for WME. We also show the reverse: if the system is WME, then the condition is satisfied for some (sufficiently large) volume. Simultaneously, we obtain an ex...
• An isoperimetric inequality on the discrete cube, and an elementary proof of the isoperimetric inequality in Gauss space AI翻译
  作者：Bobkov, SG
  作者单位：Syktyvkar State University
  摘要：We prove an isoperimetric inequality on the discrete cube which is the precise analog of a logarithmic inequality due to Talagrand. As a consequence, the Gaussian isoperimetric inequality is derived.
• Asymptotics of a class of Markov processes which are not in general irreducible (vol 16, pg 1333, 1988) AI翻译
  作者：Bhattacharya, RN; Lee, O
  作者单位：Indiana University System; Indiana University Bloomington
  摘要：The set P(S) of probability measures on the Borel sigma field of every closed subset S of R-k is shown to be complete under a Kolmogorov type metric. An assertion in the 1988 article by Bhattacharya and Lee that this completeness holds if S is merely topologically complete is false.
• When is a probability measure determined by infinitely many projections? AI翻译
  作者：Bélisle, C; Massé, JC; Ransford, T
  作者单位：Laval University
  摘要：The well-known Cramer-Wold theorem states that a Borel probability measure on R-d is uniquely determined by the totality of its one-dimensional projections. In this paper we examine various conditions under which a probability measure is determined by a subset of its (d - 1)-dimensional orthogonal projections.