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作者：Lalley, SP
作者单位：University of Chicago
摘要：The p-shuffle is a natural generalization of the dovetail shuffle. It is defined as follows. First, the deck is cut into a top stack and a bottom stack so that the distribution of the size of the top stack is Binomial (N, p), where N is the total number of cards in the deck Then, conditional on the outcome of the cut, the two stacks are riffled in such a way that all possible riffles (interleavings) of these two stacks are equally likely The main result of the paper is an asymptotic (N --> in...
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作者：Fusai, G
作者单位：University of Florence
摘要：We study a generalization of the are-sine law In particular we provide new results about the distribution of the time spent by a BM with drift inside a band, giving the Laplace transform of the characteristic function. If one of the extremes of the band goes to infinity, our formula agrees with the results given in Akahori and Takacs. We apply these results to the pricing of exotic option contracts known as corridor derivatives. We then discuss the inversion problem comparing different numeric...
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作者：Baryshnikov, YM; Gnedin, AV
作者单位：Eindhoven University of Technology; University of Gottingen
摘要：Let random points X-1,...,X-n be sampled in strict sequence from a continuous product distribution on Euclidean d-space. At the time X-j is observed it must be accepted or rejected. The subsequence of accepted points must increase in each coordinate. We show that the maximum expected length of a subsequence selected is asymptotic to gamman(1/(d+1)) and give the exact value of gamma. This extends the root 2n result by Samuels and Steele for d = 1.
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作者：Harrison, JM
作者单位：Stanford University
摘要：A recent paper by Harrison and Van Mieghem explained in general mathematical terms how one forms an equivalent workload formulation of a Brownian network model. Denoting by Z(t) the state vector of the original Brownian network, one has a lower dimensional state descriptor W(t) = MZ(t) in the equivalent workload formulation, where M can be chosen as any basis matrix for a particular linear space. This paper considers Brownian models for a very general class of open processing net works, and in...
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作者：Burdzy, K; Kendall, WS
作者单位：University of Washington; University of Washington Seattle; University of Warwick
摘要：In this paper we study the notion of an efficient coupling of Markov processes. Informally, an efficient coupling is one which couples at the maximum possible exponential rate, as given by the spectral gap. This notion is of interest not only for its own sake, but also of growing importance arising from the recent advent of methods of perfect simulation: it helps to establish the price of perfection for such methods. In general, one can always achieve efficient coupling if the coupling is allo...
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作者：Graham, C; O'Connell, N
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; Hewlett-Packard
摘要：We consider a symmetric network composed of N links, each with capacity C. Calls arrive according to a Poisson process, and each call concerns L distinct links chosen uniformly at random. If each of these links has free capacity, the call is held for an exponential time; otherwise it is lost. The semiexplicit stationary distribution for this process is similar to a Gibbs measure: it involves a normalizing factor, the partition function, which is very difficult to evaluate. We let N go to infin...
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作者：Fontes, LR; Mathieu, P; Picco, P
作者单位：Universidade de Sao Paulo; Aix-Marseille Universite; Aix-Marseille Universite
摘要：We describe the averaged over the disordered dynamics for the random field Curie-Weiss model. We consider both the magnetization and the full spin dynamics. Our approach is based on spectral asymptotics and includes results on the random fluctuations of eigenvalues and eigenvectors.
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作者：Gärtner, J; König, W
作者单位：Technical University of Berlin
摘要：We consider the parabolic Anderson problem partial derivative (t)u = kappa Deltau + xi (x)u on R+ x R-d with initial condition u(0, x) = 1. Here xi(.) is a random shift-invariant potential having high delta -like peaks on small islands. We express the second-order asymptotics of the pth moment (p is an element of [1, infinity)) of u(t, 0) as t --> infinity in terms of a variational formula involving an asymptotic description of the rescaled shapes of these peaks via their cumulant generating f...
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作者：Baccelli, F; Hong, D
作者单位：Universite PSL; Ecole Normale Superieure (ENS)
摘要：We give an explicit analytic series expansion of the (max, plus)Lyapunov exponent gamma (p) of a sequence of independent and identically distributed random matrices, generated via a Bernoulli scheme depending on a small parameter p. A key assumption is that one of the matrices has a unique normalized eigenvector. This allows us to obtain a representation of this exponent as the mean value of a certain random variable. We then use a discrete analogue of the so-called light-traffic perturbation ...
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作者：Hofmann, N; Müller-Gronbach, T; Ritter, K
作者单位：University of Passau; Free University of Berlin; University of Erlangen Nuremberg
摘要：We analyze the pathwise approximation for systems of stochastic differential equations. The pathwise distance between the solution and its approximation is measured globally on the unit interval in the L-infinity-norm, and we study the expectation of this distance. For systems with additive noise we obtain sharp lower and upper bounds for the minimal error in the class of arbitrary methods which use discrete observations of a Brownian path. The optimal order is achieved by an Euler scheme with...
