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• 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...
• 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.
• Long time existence for the wave equation with a noise term AI翻译
  作者：Mueller, C
  作者单位：University of Rochester
  摘要：We consider the equation u(tt) = Delta u + a(u)N for x is an element of R-1 or R-2. N is a Gaussian noise term, which is white noise if x is an element of R-1. If a(u) grows no faster than u(log u)(1/2-epsilon), then there is a unique solution valid for all time.
• Self-normalized large deviations AI翻译
  作者：Shao, QM
  作者单位：University of Oregon
  摘要：Let {X, X-n, n greater than or equal to 1} be a sequence of independent and identically distributed random variables. The classical Cramer-Chernoff large deviation states that lim(n-->infinity) n(-1) ln P((Sigma(i=1)(n) X-i)/n greater than or equal to x) = ln rho(x) if and only if the moment generating function of X is finite in a right neighborhood of zero. This paper uses n((p-1)/p)V(n,p) = n((p-1)/p)(Sigma(i=1)(n) \X-i\(p))(1/p) (p > 1) as the normalizing constant to establish a self-normal...
• Approximation of subadditive functions and convergence rates in limiting-shape results AI翻译
  作者：Alexander, KS
  作者单位：University of Southern California
  摘要：For a nonnegative subadditive function h on Z(d), with limiting approximation g(x) = lim(n) h(nx)/n, it is of interest to obtain bounds on the discrepancy between g(x) and h(x), typically of order \x\(nu) with nu < 1. For certain subadditive h(x), particularly those which are expectations associated with optimal random paths from 0 to x, in a somewhat standardized way a more natural and seemingly weaker property can be established: every x is in a bounded multiple of the convex hull of the set...
• Nested classes of C-decomposable laws AI翻译
  作者：Bunge, J
  作者单位：Cornell University
  摘要：A random variable X is C-decomposable if X = (D) cX + Y-c for all c in C, where Y-c is a random variable independent of X and C is a closed multiplicative subsemigroup of [0, 1]. X is self-decomposable if C = [0, 1]. Extending an idea of Urbanik in the self-decomposable case, we define a decreasing sequence of subclasses of the class of C-decomposable laws, for any C. We give a structural representation for laws in these classes, and we show that laws in the limiting subclass are infinitely di...
• On moderate deviations for martingales AI翻译
  作者：Grama, IG
  作者单位：Academy of Sciences of Moldova
  摘要：Let X-n = (X-t(n), F-t(n))(0 less than or equal to t less than or equal to 1) be square integrable martingales with the quadratic characteristics [X-n], n = 1, 2, .... We prove that the large deviations relation P(X-1(n) greater than or equal to r)/(1 - Phi(r)) --> 1 holds true for r growing to infinity with some rate depending on L-2 delta(n) = E Sigma(0 less than or equal to t less than or equal to 1) \Delta X-t(n)\(2+2 delta) and N-2 delta(n) = E\[X-n](1) - 1\(1+delta), where delta > 0 and ...
• The random difference equation Xn = AnXn-1+Bn in the critical case AI翻译
  作者：Babillot, M; Bougerol, P; Elie, L
  作者单位：Sorbonne Universite; Universite Paris Cite
  摘要：Let (B-n, A(n))(n greater than or equal to 1) be a sequence of i.i.d. random variables with values in R-d x R-*(+). The Markov chain on R-d which satisfies the random equation X-n = A(n)X(n-1) + B-n is studied when E(log A(1)) = 0. No density assumption on the distribution of (B-1, A(1)) is made. The main results are recurrence of the Markov chain X-n, stability properties of the paths, existence and uniqueness of a Radon invariant measure and a limit theorem for the occupation times. The resu...
• Domination by product measures AI翻译
  作者：Liggett, TM; Schonmann, RH; Stacey, AM
  作者单位：University of California System; University of California Los Angeles
  摘要：We consider families of {0, 1}-valued random variables indexed by the vertices of countable graphs with bounded degree. First we show that if these random variables satisfy the property that conditioned on what happens outside of the neighborhood of each given site, the probability of seeing a 1 at this site is at least a value p which is large enough, then this random field dominates a product measure with positive density. Moreover the density of this dominated product measure can be made ar...