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作者：Foss, S; Zachary, S
作者单位：Heriot Watt University
摘要：We study the asymptotics for the maximum on a random time interval of a random walk with a long-tailed distribution of its increments and negative drift. We extend to a general stopping time a result by Asmussen, simplify its proof and give some converses.
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作者：Gajrat, A; Hordijk, A; Ridder, A
作者单位：Leiden University - Excl LUMC; Leiden University
摘要：A fluid approximation gives the main term in the asymptotic expression of the value function for a controllable stochastic network. The policies that have the same asymptotic of their value functions as the value function of the optimal policy are called asymptotically optimal policies. We consider the problem of finding from this set of asymptotically optimal policies a best one in the sense that the next term of its asymptotic expression is minimal. The analysis of this problem is closely co...
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作者：Rabehasaina, L; Sericola, B
作者单位：Universite Paris Saclay; Universite de Rennes
摘要：In this paper, we study the stability of a fluid queue with an infinite-capacity buffer. The input and service rates are governed by a stochastic process, called the environment process, and are allowed to depend on the fluid level in the buffer. The variability of the traffic is modeled by a Brownian motion and a local variance function, which also depends on the fluid level in the buffer. The behavior of this second-order fluid flow model is described by a reflected stochastic differential e...
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作者：MacPhee, IM; Menshikov, MV
作者单位：Durham University
摘要：We consider a time-homogeneous random walk Xi = {xi (t)} on a two-dimensional complex. All of our results here are formulated in a constructive way. By this we mean that for any given random walk we can, with an expression using only the first and second moments of the jumps and the return probabilities for some transient one-dimensional random walks, conclude whether the process is ergodic, null-recurrent or transient. Further we can determine when pth moments of passage times tau(K) to sets ...
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作者：Resnick, S; Samorodnitsky, G
作者单位：Cornell University
摘要：A hierarchical product model seeks to model network traffic as a product of independent on/off processes. Previous studies have assumed a Markovian structure for component processes amounting to assuming that exponential distributions govern on and off periods, but this is not in good agreement with traffic measurements. However, if the number of factor processes grows and input rates are stabilized by allowing the on period distribution to change suitably, a limiting on/off process can be obt...
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作者：Kyprianou, AE; Pistorius, MR
作者单位：Utrecht University; University of London; King's College London
摘要：In this article it is shown that one is able to evaluate the price of perpetual calls, puts, Russian and integral options directly as the Laplace transform of a stopping time of an appropriate diffusion using standard fluctuation theory. This approach is offered in contrast to the approach of optimal stopping through free boundary problems. Following ideas of Carr [Rev. Fin. Studies 11 (1998) 597-626], we discuss the Canadization of these options as a method of approximation to their finite ti...
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作者：Eibeck, A; Wagner, W
作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics
摘要：We present the stochastic approach to nonlinear kinetic equations (without gradient terms) in a unifying general framework, which covers many interactions important in applications, such as coagulation, fragmentation, inelastic collisions, as well as source and efflux terms. We provide conditions for the existence of corresponding stochastic particle systems in the sense of regularity (nonexplosion) of a jump process with unbounded intensity. Using an appropriate space of measure-valued functi...
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作者：Booth, L; Bruck, J; Franceschetti, M; Meester, R
作者单位：Utrecht University; California Institute of Technology; Vrije Universiteit Amsterdam
摘要：Continuum percolation models in which each point of a two-dimensional Poisson point process is the centre of a disc of given (or random) radius r, have been extensively studied. In this paper, we consider the generalization in which a deterministic algorithm (given the points of the point process) places the discs on the plane, in such a way that each disc covers at least one point of the point process and that each point is covered by at least one disc. This gives a model for wireless communi...
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作者：Guo, XP; Hernández-Lerma, O
作者单位：Sun Yat Sen University; CINVESTAV - Centro de Investigacion y de Estudios Avanzados del Instituto Politecnico Nacional; Instituto Politecnico Nacional - Mexico
摘要：This paper concerns studies on continuous-time controlled Markov chains, that is, continuous-time Markov decision processes with a denumerable state space, with respect to the discounted cost criterion. The cost and transition rates are allowed to be unbounded and the action set is a Borel space. We first study control problems in the class of deterministic stationary policies and give very weak conditions under which the existence of epsilon-optimal (epsilon greater than or equal to 0) polici...
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作者：Cohn, H; Wang, Q
作者单位：University of Melbourne
摘要：For a multitype branching process in varying environment convergent in probability, a certain sequence of linear combinations of the type sizes is shown to possess some convergence properties. This sequence turns out to be instrumental in deriving a condition for continuity of the limiting distribution function. An application to an L-1 convergent process whose offspring mean matrices are weakly ergodic is also given.
