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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...
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作者：FERRARI, PA; KESTEN, H; MARTINEZ, S; PICCO, P
作者单位：Universidad de Chile; Cornell University; Centre National de la Recherche Scientifique (CNRS); Aix-Marseille Universite
摘要：We consider Markov processes on the positive integers for which the origin is an absorbing state. Quasi-stationary distributions (qsd's) are described as fixed points of a transformation Phi in the space of probability measures. Under the assumption that the absorption time at the origin, R, of the process starting from state x goes to infinity in probability as x --> infinity, Pie show that the existence of a qsd is equivalent to E(x)e(lambda R) < infinity for some positive lambda and x. We a...
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作者：LIGGETT, TM
摘要：The best known upper bound for the critical value lambda(c) of the basic one dimensional contact process is 2. Most techniques for finding bounds on critical values have the property that they can be modified in order to obtain improved bounds. This seemed not to be the case for the approach which yielded lambda(c) less than or equal to 2 for the basic contact process. In this paper, we propose a technique for generating better bounds in this context. To illustrate its use, we carry out the fu...
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作者：DURRETT, R; SCHINAZI, R
作者单位：University of Colorado System; University of Colorado at Colorado Springs
摘要：We show that in between the two critical values for the contact process on trees, there are infinitely many extremal nontranslation invariant stationary distributions. This conclusion is reminiscent of results of Grimmett and Newman for percolation on the product of a tree with the integers where there is an intermediate phase with infinitely many infinite clusters.
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作者：EINMAHL, U
摘要：In a recent paper by the author it has been shown that there exists a general law of the iterated logarithm (LIL) in Banach space, which contains the LIL of Ledoux and Talagrand and an LIL for infinite-dimensional random variables in the domain of attraction to a Gaussian law as special cases. We now investigate the corresponding cluster set problem, which we completely solve for random vectors in two-dimensional Euclidean space. Among other things, we show that all cluster sets arising from t...
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作者：KALPAZIDOU, S
摘要：Let (S-i, i = 1, 2,..., n), n > 1, be a partition of the circle into sets S-i each consisting of union of delta(i) < infinity, arcs A(kl). Let f(t) be a rotation of length t of the circle and denote Lebesgue measure by lambda. Then every recurrent stochastic matrix P on S = {1,..., n} is given according to a theorem of Cohen (n = 2), Alpern and Kalpazidou (n greater than or equal to 2) by p(ij) = lambda S-i boolean AND f(t)(-1)(S-j))/lambda(Si) for some choice of rotation f(t) and partition L ...
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作者：MONAT, P; STRICKER, C
摘要：Let X be an R(d)-valued special semimartingale on a probability space (Omega,F,(F-t)(0 less than or equal to t less than or equal to T), P) with decomposition X = X(0) + M + A and Theta the space of all predictable, X-integrable processes theta such that integral theta dX is in the space P-2 of semimartingales. If H is a random variable in L(2), We prove, under additional assumptions on the process X, that H can be written as the sum of an F-0-measurable random variable H-0, a stochastic integ...
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作者：DEUSCHEL, JD; ZEITOUNI, O
作者单位：Technion Israel Institute of Technology
摘要：We consider the concentration of measure for n i.i.d., two-dimensional random variables under the conditioning that they form a record. Under mild conditions, we show that all random variables tend to concentrate, as n --> infinity, around Limiting curves, which are the solutions of an appropriate variational problem. We also show that the same phenomenon occurs, without the records conditioning, for the longest increasing subsequence in the sample.
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作者：WANG, G
摘要：Let X and Y be two continuous-time martingales. If quadratic variation of X minus that of Y is a nondecreasing and nonnegative function of time, we say that Y is differentially subordinate to X and prove that \\Y\\(p) less than or equal to (p* - 1)\\X\\(p) for 1 < p < infinity, where p* = p boolean OR q and q is the conjugate of p. This inequality contains Burkholder's L(p)-inequality for stochastic integrals, which implies that the above inequality is sharp. We also extend his concept, of str...
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作者：KENDALL, WS
摘要：An upper bound is given for the behaviour of the radial part of a Gamma-martingale, generalizing previous work of the author on the radial part of Riemannian Brownian motion. This upper bound is applied to establish an integral curvature condition to determine when Gamma-martingales cannot ''implode'' in finite intrinsic time, answering a question of Emery and generalizing work of Hsu on the C-0-diffusion property of Brownian motion.
