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作者：Yu, H
摘要：By combining the Berbes-Philipp blocking technique and the Csorgo-Revesz quantile transform methods, we find that partial sums of an associated sequence can be approximated almost surely by partial sums of another sequence with Gaussian marginals. A crucial fact is that this latter sequence is still associated with covariances roughly bounded by the covariances of the original sequence, and that one can approximate it by an lid Gaussian process using the Berkes-Philipp method. We require that ...
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作者：Renz, J
作者单位：Michigan State University
摘要：Bolthausen established a bound of order 1/root n on the rate of convergence in the central limit theorem for martingale difference arrays having bounded conditional moments of order 4. In the present paper it is shown how much this moment condition can be relaxed while maintaining the same rate of convergence. An example shows that, unlike in the i.i.d. case, a moment condition of order 3 is not enough. Furthermore, exact rates of convergence are derived for moment conditions of order between ...
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作者：Zhang, Y
摘要：Consider the contact process on a homogeneous tree with degree d greater than or equal to 3. Denote by lambda(c) = inf{lambda:P(o is an element of xi i.o.) > 0} the critical value of local survival probability, where o is the root of the tree. Pemantle and Durrett and Schinazi both conjectured that the complete convergence theorem should hold if lambda > lambda(c). Here we answer the conjecture affirmatively. Furthermore, we will show that P(o is an element of xi(t)(o) i.o.) = 0 at lambda(c). ...
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作者：Flandoli, F
摘要：The existence of stochastic flows in L(2)-spaces is proved for a stochastic reaction-diffusion equation of second order in a bounded domain.
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作者：Khoshnevisan, D; Lewis, TM; Shi, Z
作者单位：Sorbonne Universite
摘要：Let {S-n, n greater than or equal to 0} be a centered d-dimensional random walk (d greater than or equal to 3) and consider the so-called future infima process J(n) =(df)inf(k greater than or equal to n) \\S-k\\. This paper is concerned with obtaining precise integral criteria for a function to be in the Levy upper class of J. This solves an old problem of Erdos and Taylor, who posed the problem for the simple symmetric random walk on Z(d), d greater than or equal to 3. These results are obtai...
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作者：Schweizer, M
摘要：Let X be a semimartingale and let Theta be the space of all predictable X-integrable processes theta such that integral theta dX is in the space L(2) of semimartingales. We consider the problem of approximating a given random variable H is an element of L(2)(P) by the sum of a constant c and a stochastic integral integral(0)(T) theta(s), dX(s), with respect to the L(2)(P)-norm. This problem comes from financial mathematics, where the optimal constant V-0 can be interpreted as an approximation ...
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作者：vanderVaart, A
摘要：Several classes of functions are shown to be Donsker by an argument based on partitioning the sample space. One example is the class of all nondecreasing functions f: R --> R such that 0 less than or equal to f less than or equal to F for a given function F with integral F-2 dP/root 1 - P < infinity.
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作者：Bovier, A; Gayrard, V
作者单位：Aix-Marseille Universite
摘要：We prove a large deviation principle for the finite-dimensional marginals of the Gibbs distribution of the macroscopic ''overlap'' parameters in the Hopfield model in the case where the number of random ''patterns'' M, as a function of the system size N, satisfies lim sup M(N)/N = 0. In this case, the rate function is independent of the disorder for almost all realizations of the patterns.
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作者：Haggstrom, O; Meester, R
作者单位：Utrecht University
摘要：This paper deals with first passage percolation where the usual i.i.d. condition is weakened to stationarity (and ergodicity). The well known asymptotic shape result is known to extend to this case. It is easy to give necessary conditions for a compact set B subset of R(d) to arise as the asymptotic shape for some stationary measure on the passage times. Our main result says that these conditions are also sufficient.
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作者：DELAPENA, VH; MONTGOMERYSMITH, SJ
作者单位：University of Missouri System; University of Missouri Columbia
摘要：In this paper we present a decoupling inequality that shows that multivariate U-statistics can be studied as sums of(conditionally) independent random variables. This result has important implications in several areas of probability and statistics including the study of random graphs and multiple stochastic integration. More precisely, we get the following result: Let {X(j)} be a sequence of independent random variables on a measurable space (L, S) and let {X(i)((j))}, j = 1,..., k, be k indep...
