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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.
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作者：Mézières, S; Roynette, B
作者单位：Universite de Lorraine
摘要：This paper is concerned with the simulation of a a-dimensional stochastic differential equation motivated by some physical phenomena of fluid mechanics. The drift and diffusion coefficients of the equation admitting local singularities, we are led to study a particular term of strong perturbation denoted by Brownian impulse. Our suggestion for the simulation is to replace the singularity by a jump on which our study therefore focuses.
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作者：Fournier, N
作者单位：Universite Paris Cite; Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We consider a two-dimensional Kac equation without cutoff, which we relate to a stochastic differential equation. We prove the existence of a solution for this SDE, and we use the Malliavin calculus (or stochastic calculus of variations) to prove that the law of this solution admits a smooth density with respect to the Lebesgue measure on R-2. This density satisfies the Kac equation.
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作者：Kumar, S
作者单位：Stanford University
摘要：One of the successes of the Brownian approximation approach to dynamic control of queueing networks is the design of a control policy for closed networks with two servers by Harrison and Wein. Adopting a Brownian approximation with only heuristic justification, they interpret the optimal control policy for the Brownian model as a static priority rule and conjecture that this priority rule is asymptotically optimal as the closed networks's population becomes large. This paper studies closed que...
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作者：Glazebrook, KD; Wilkinson, DJ
作者单位：Newcastle University - UK
摘要：We utilize and develop elements of the recent achievable region account of Gittins indexation by Bertsimas and Nino-Mora to design index-based policies for discounted multi-armed bandits on parallel machines. The policies analyzed have expected rewards which come within an O(alpha) quantity of optimality, where alpha > 0 is a discount rate. In the main, the policies make an initial once for all allocation of bandits to machines, with each machine then handling its own workload optimally. This ...
