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作者：Drees, H
作者单位：Ruprecht Karls University Heidelberg
摘要：While the extreme value statistics for i.i.d data is well developed, much less is known about the asymptotic behavior of statistical procedures in the presence of dependence. We establish convergence of the tail empirical processes to Gaussian limits for beta -mixing stationary time series. As a consequence, one obtains weighted approximations of the tail empirical quantile function that is based on a random sequence with marginal distribution belonging to the domain of attraction of an extrem...
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作者：Zeevi, AJ; Glynn, PW
作者单位：Stanford University; Stanford University
摘要：Consider a queue with a stochastic fluid input process modeled as fractional Brownian motion (fBM). When the queue is stable, we prove that the maximum of the workload process observed over an interval of length t grows like gamma (logt)(1/(2-2H)), where H > 1/2 is the self-similarity index (also known as the Hurst parameter) that characterizes the fBM and can be explicitly computed. Consequently, we also have that the typical time required to reach a level b grows like exp{b(2(1-H))}. We also...
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作者：Diaconis, P; Holmes, S; Neal, RM
作者单位：Stanford University; INRAE; University of Toronto; University of Toronto
摘要：We analyze the convergence to stationarity of a simple nonreversible Markov chain that serves as a model for several nonreversible Markov chain sampling methods that are used in practice. Our theoretical and numerical results show that nonreversibility can indeed lead to improvements over the diffusive behavior of simple Markov chain sampling schemes. The analysis uses both probabilistic techniques and an explicit diagonalization.
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作者：Touzi, N
作者单位：Universite PSL; Universite Paris-Dauphine; Institut Polytechnique de Paris; ENSAE Paris
摘要：We study the stochastic control problem of maximizing expected utility from terminal wealth, when the wealth process is subject to shocks produced by a general marked point process; the problem of the agent is to derive the optimal allocation of his wealth between investments in a nonrisky asset and in a (costly) insurance strategy which allows lowering the level of the shocks. The agent's optimization problem is related to a suitable dual stochastic control problem in which the constraint on ...
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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...
