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作者：Breidt, FJ; Davis, RA
作者单位：Iowa State University; Colorado State University System; Colorado State University Fort Collins
摘要：Extreme value theory for a class of stochastic volatility models, in which the logarithm of the conditional variance follows a Gaussian linear process, is developed. A result for the asymptotic tail behavior of the transformed stochastic volatility process is established and used to prove that the suitably normalized extremes converge in distribution to the double exponential (Gumbel) distribution. Explicit normalizing constants are obtained, and point process convergence is discussed.
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作者：Hobson, DG
作者单位：University of Bath
摘要：Consider the performance of an options writer who misspecifies the dynamics of the price process of the underlying asset by overestimating asset price volatility. When does he overprice the option? If he follows the hedging strategy suggested by his model, when does the terminal value of his strategy dominate the option payout? We show that both these events happen if the option payoff is a convex function of the price of the underlying at maturity. The proofs involve the simple, powerful and ...
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作者：Feng, S; Hoppe, FM
作者单位：McMaster University
摘要：Large deviation principles are established for some random combinatorial structures including the Ewens sampling formula and the Pitman sampling formula. A path-level large deviation principle is established for the former on the cadlag space D([0, 1], R) equipped with the uniform convergence topology, and the rate function is the same as for a Poisson process justifying the Poisson process approximation for the Ewens sampling formula at the large deviation level. A large deviation principle f...
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作者：Zerner, MPW
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We derive a shape theorem type result for the almost sure exponential decay of the Green's function of -Delta + V, where the potentials V(x), x is an element of Z(d), are i.i.d. nonnegative random variables. This result implies a large deviation principle governing the position of a d-dimensional random walk moving in the same potential.
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作者：Chang, KH; Serfozo, RF; Szczotka, W
作者单位：Chung Yuan Christian University; University System of Georgia; Georgia Institute of Technology; University of Wroclaw
摘要：This study establishes limiting distributions for customer waiting times and queue lengths in treelike networks with single-server nodes. The main result characterizes the limiting distributions when the network data (interarrival times, service times and routes) is asymptotically stationary. This is a weak condition covering a variety of networks including standard ones where the network data is stationary, regenerative, Markovian, satisfies coupling, and so on. The dependencies in the networ...
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作者：Massey, WA; Whitt, W
作者单位：Nokia Corporation; Nokia Bell Labs; Alcatel-Lucent; Lucent Technologies; AT&T; AT&T
摘要：We study uniform acceleration (UA) expansions of finite-state continuous-time Markov chains with time-varying transition rates. The UA expansions can be used to justify evaluate and reline the pointwise stationary approximation, which is the steady-state distribution associated with the time-dependent generator at the time of interest. We obtain UA approximations from these UA asymptotic expansions. We derive a time-varying analog to the uniformization representation of transition probabilitie...
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作者：Alanyali, M; Hajek, B
作者单位：AT&T; Alcatel-Lucent; Lucent Technologies; University of Illinois System; University of Illinois Urbana-Champaign; University of Illinois System; University of Illinois Urbana-Champaign
摘要：Three policies, namely optimal repacking, least load routing, and Bernoulli splitting, are considered for dynamic resource allocation in load sharing networks with standard Erlang type statistics. Large deviations principles are established for the three policies in a simple network of three consumer types and two resource locations and are used to identify the network overflow exponents. The overflow exponents for networks with arbitrary topologies are identified for optimal repacking and Ber...
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作者：Klebaner, FC; Lazar, J; Zeitouni, O
作者单位：University of Melbourne; University of Melbourne; Technion Israel Institute of Technology
摘要：We consider a Markov chain X-n(epsilon) obtained by adding small noise to a discrete time dynamical system and study the chain's quasi-stationary distribution (qsd). The dynamics are given by iterating a function f: I --> I for some interval I when f has finitely many fixed points, some stable and some unstable. We show that under some conditions the quasi-stationary distribution of the chain concentrates around the stable fixed points when epsilon --> 0. As a corollary, we obtain the result f...
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作者：Bertsimas, D; Paschalidis, IC; Tsitsiklis, JN
作者单位：Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT); Boston University
摘要：We consider a single class, acyclic network of G/G/1 queues. We impose some mild assumptions on the service and external arrival processes and we characterize the large deviations behavior of all the processes resulting from various operations in the network. For the network model that we are considering, these operations are passing-through-a-single-server-queue (the process resulting from this operation being the departure process), superposition of independent processes and deterministic sp...
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作者：Yakir, B; Pollak, M
作者单位：Hebrew University of Jerusalem
摘要：The probability that a stochastic process with negative drift exceed a value a often has a renewal-theoretic approximation as a --> infinity. Except for a process of iid random variables, this approximation involves a constant which is not amenable to analytic calculation. Naive simulation of this constant has the drawback of necessitating a choice of finite a, thereby hurting assessment of the precision of a Monte Carlo simulation estimate, as the effect of the discrepancy between a and infin...
