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作者：Karatzas, I; Sudderth, WD
作者单位：Columbia University; University of Minnesota System; University of Minnesota Twin Cities
摘要：Consider a process X(.) = {X(t), 0 less than or equal to t < infinity} which takes values in the interval I = (0, 1), satisfies a stochastic differential equation dX(t) = beta(t) dt + sigma(t) dW(t), X(0) = x is an element of I and, when it reaches an endpoint of the interval I, it is absorbed there. Suppose that the parameters beta and sigma are selected by a controller at each instant t is an element of [0, infinity) from a set depending on the current position. Assume also that the controll...
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作者：Norris, JR
作者单位：University of Cambridge
摘要：Sufficient conditions are given for existence and uniqueness in Smoluchowski's coagulation equation, for a wide class of coagulation kernels and initial mass distributions. An example of nonuniqueness is constructed. The stochastic coalescent is shown to converge weakly to the solution of Smoluchowski's equation.
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作者：Iglói, E; Terdik, G
作者单位：University of Debrecen
摘要：The partial derivatives with respect to time and the fractional Brownian motion of a particular class of stationary processes are defined. Although the fractional Brownian motion is not semimartingale, the bilinear SDE with fractional Brownian motion input is considered and solved. The solution is explicitly given in both the frequency and time domains in the case when the coefficient of the bilinear term is pure imaginary. The stationary Stratonovich solution of the bilinear SDE with white no...
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作者：Fulman, J; Wilmer, EL
作者单位：Harvard University
摘要：The Poincare and Cheeger bounds are two useful bounds for the second largest eigenvalue of a reversible Markov chain. Diaconis and Stroock and Jerrum and Sinclair develop versions of these bounds which involve choosing paths. This paper studies these path-related bounds and shows that the Poincare bound is superior to the Cheeger bound for simple random walk on a tree and random walk on a finite group with any symmetric generating set. This partially resolves a question posed by Diaconis and S...
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作者：Frieze, A; Kannan, R
作者单位：Carnegie Mellon University; Carnegie Mellon University
摘要：We consider the problem of sampling according to a distribution with log-concave density F over a convex body K subset of or equal to R-n. The sampling is done using a biased random walk and we give improved polynomial upper bounds on the time to get a sample point with distribution close to F.
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作者：Horváth, L; Shao, QM
作者单位：Utah System of Higher Education; University of Utah; University of Oregon
摘要：We establish strong and weak approximations for quadratic forms of weakly and strongly dependent random variables and obtain necessary and sufficient conditions for the weak convergence of weighted functions of quadratic forms. The results are applied to get the asymptotic distributions of some tests which can be used to detect possible changes in the long-memory parameter.
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作者：Jones, BD; Pittel, BG; Verducci, JS
作者单位：University System of Ohio; Kenyon College; University System of Ohio; Ohio State University; University System of Ohio; Ohio State University
摘要：For a complete graph K-n on n vertices with weighted edges, define the weight of a spanning tree (more generally, spanning forest) as the product of edge weights involved. Define the tree weight (forest weight) of K-n as the total weight of all spanning trees (forests). The uniform edge weight distribution is shown to maximize the tree weight, and an explicit bound on the tree weight is formulated in terms of the overall variance of edge weights as well as the variance of the sum of edge weigh...
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作者：Stein, ML
作者单位：University of Chicago
摘要：This work investigates some spectral characteristics of the errors of optimal linear predictors for weakly stationary random fields. More specifically, for errors of optimal linear predictors, results here explicitly bound the fraction of the variance attributable to some set of frequencies. Such a bound is first obtained for random fields on R-d observed on the infinite lattice delta J for all J on the d-dimensional integer lattice. If the spectral density exists, then the faster the spectral...
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作者：McDonald, DR
作者单位：University of Ottawa
摘要：We wish to describe how a chosen node in a network of queues overloads. The overloaded node may also drive other nodes into overload, but the remaining super stable nodes are only driven into a new steady state with stochastically larger queues. We model this network of queues as a Markov additive chain with a boundary. The customers at the super stable nodes are described by a Markov chain, while the other nodes are described by an additive chain. We use the existence of a harmonic function h...
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作者：Yukich, JE
作者单位：Lehigh University
摘要：Given F subset of [0, 1](2) and finite, let a(F) denote the length of the minimal Steiner triangulation of points in F. By showing that minimal Steiner triangulations fit into the theory of subadditive and superadditive Euclidean functionals, we prove under a mild regularity condition that lim(n --> infinity) sigma(X-1..., X-n)/n(1/2) = beta integral([0, 1]2)f(x)(1/2) DX c.c., where X-1,...,X-n are i.i.d. random variables with values in [0, 1](2), beta is a positive constant, f is the density ...
