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作者：Resnick, S; Rootzén, H
作者单位：Cornell University; Chalmers University of Technology
摘要：Several studies of file sizes either being downloaded or stored in the World Wide Web have commented that tails can be so heavy that not only are variances infinite, but so are means. Motivated by this fact, we study the infinite node Poisson model under the assumption that transmission times are heavy tailed with infinite mean. The model is unstable but we are able to provide growth rates. Self-similar but nonstationary Gaussian process approximations are provided for the number of active sou...
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作者：Liu, QS; Rouault, A
作者单位：Universite de Rennes; Universite Paris Saclay
摘要：Let W greater than or equal to 0 be a random variable with EW = 1, and let Z((r)) (r greater than or equal to 2) be the limit of a Mandelbrot's martingale, defined as sums of product of independent random weights having the same distribution as W, indexed by nodes of a homogeneous r-ary tree. We study asymptotic properties of Z((r)) as r --> infinity: we obtain a law of large numbers, a central limit theorem, a result for convergence of moment generating functions and a theorem of large deviat...
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作者：Maglaras, C
作者单位：Columbia University
摘要：This paper describes a general approach for dynamic control of stochastic networks based an fluid model analysis, where in broad terms, the stochastic network is approximated by its fluid analog, an associated fluid control problem is solved and, finally, a scheduling rule for the original system is defined by interpreting the fluid control policy. The main contribution of this paper is to propose a general mechanism for translating the solution of the fluid optimal control problem into an imp...
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作者：Mykland, PA
作者单位：University of Chicago
摘要：It is common to have interval predictions for volatilities and other quantities governing securities prices. The purpose of this paper is to provide an exact method for converting such intervals into arbitrage based prices of financial derivatives or industrial or contractual options. We call this procedure conservative delta hedging. The proposed approach will permit an institution's management a greater oversight of its exposure to risk.
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作者：Adler, RJ
作者单位：Technion Israel Institute of Technology
摘要：This is a rambling review of what, with a few notable and significant exceptions, has been a rather dormant area for over a decade. It concentrates on the septuagenarian problem of finding good approximations for the excursion probability P{sup(t is an element ofT) X-t greater than or equal to lambda}, where lambda is large, X is a Gaussian, or Gaussian-like, process over a region T subset of R-N and, generally, N > 1. A quarter of a century ago, there was a flurry of papers out of various sch...
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作者：Papangelou, F
作者单位：University of Manchester; National & Kapodistrian University of Athens
摘要：This is the fourth in a series of papers devoted to the study of the large deviations of a Wright-Fisher process modeling the genetic evolution of a reproducing population. Variational considerations imply that if the process undergoes a large deviation, then it necessarily follows closely a definite path from its original to its current state. The favored paths were determined previously for a one-dimensional process subject to oneway mutation or natural selection, respectively, acting on a f...
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作者：Mikosch, T; Smorodnitsky, G
作者单位：University of Groningen; Cornell University
摘要：Many important probabilistic models in queuing theory, insurance and finance deal with partial sums of a negative mean stationary process (a negative drift random walk), and the law of the supremum of such a process is used to calculate, depending on the context, the ruin probability, the steady state distribution of the number of customers in the system or the value at risk. When the stationary process is heavy-tailed, the corresponding ruin probabilities are high and the stationary distribut...
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作者：Perrut, A
作者单位：Universite de Rouen Normandie
摘要：We consider a reaction-diffusion process with two components, on the grid Z. This process had been introduced by Durrett and Levin to describe a two-species interaction. We prove the process admits hydrodynamic limits, first with a technique based on correlation functions, then with the method of relative entropy plus coupling.
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作者：Bäuerle, N
作者单位：Ulm University
摘要：Control problems in stochastic queuing networks are hard to solve. However, it is well known that the fluid model provides a useful approximation to the stochastic network. We will formulate a general class of control problems in stochastic queuing networks and consider the corresponding fluid optimization problem (F) which is a deterministic control problem and often easy to solve. Contrary to previous literature, our cost rate function is rather general. The value function of (F) provides an...
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作者：Boutsikas, MV; Koutras, MV
作者单位：University of Piraeus
摘要：Let X-1, X-2,..., X-n be a sequence of integer-valued random variables that are either associated or negatively associated. We present a simple upper bound for the distance between the distribution of the sum of X-i and a sum of n independent random variables with the same marginals as X-i. An upper bound useful for establishing a compound Poisson approximation for Sigma X-n(i=1)i is also provided. The new bounds are of the same order as the much acclaimed Stein-Chen bound.
