| 1. |
- Aoyama, T., et al.
(författare)
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The anomalous magnetic moment of the muon in the Standard Model
- 2020
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Ingår i: Physics reports. - : Elsevier BV. - 0370-1573 .- 1873-6270. ; 887, s. 1-166
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Forskningsöversikt (refereegranskat)abstract
- We review the present status of the Standard Model calculation of the anomalous magnetic moment of the muon. This is performed in a perturbative expansion in the fine-structure constant α and is broken down into pure QED, electroweak, and hadronic contributions. The pure QED contribution is by far the largest and has been evaluated up to and including O(α5) with negligible numerical uncertainty. The electroweak contribution is suppressed by (mμ/MW)2 and only shows up at the level of the seventh significant digit. It has been evaluated up to two loops and is known to better than one percent. Hadronic contributions are the most difficult to calculate and are responsible for almost all of the theoretical uncertainty. The leading hadronic contribution appears at O(α2) and is due to hadronic vacuum polarization, whereas at O(α3) the hadronic light-by-light scattering contribution appears. Given the low characteristic scale of this observable, these contributions have to be calculated with nonperturbative methods, in particular, dispersion relations and the lattice approach to QCD. The largest part of this review is dedicated to a detailed account of recent efforts to improve the calculation of these two contributions with either a data-driven, dispersive approach, or a first-principle, lattice-QCD approach. The final result reads aμSM = 116 591 810(43) x 10-11 and is smaller than the Brookhaven measurement by 3.7 σ. The experimental uncertainty will soon be reduced by up to a factor four by the new experiment currently running at Fermilab, and also by the future J-PARC experiment. This and the prospects to further reduce the theoretical uncertainty in the near future - which are also discussed here - make this quantity one of the most promising places to look for evidence of new physics.
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| 2. |
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| 3. |
- Asmussen, Sören, et al.
(författare)
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Asymptotics for sums of random variables with local subexponential behaviour
- 2003
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Ingår i: Journal of Theoretical Probability. - 1572-9230. ; 16:2, s. 489-518
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Tidskriftsartikel (refereegranskat)abstract
- We study distributions F on [0, infinity) such that for some T less than or equal to infinity F*(2)(x, x + T] similar to 2F(x, x + T]. The case T = infinity corresponds to F being subexponential, and our analysis shows that the properties for T < &INFIN; are, in fact, very similar to this classical case. A parallel theory is developed in the presence of densities. Applications are given to random walks, the key renewal theorem, compound Poisson process and Bellman-Harris branching processes.
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| 4. |
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| 5. |
- Asmussen, S, et al.
(författare)
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Performance analysis with truncated heavy-tailed distributions
- 2005
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Ingår i: Methodology and Computing in Applied Probability. - : Springer Science and Business Media LLC. - 1573-7713 .- 1387-5841. ; 7:4, s. 439-457
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Tidskriftsartikel (refereegranskat)abstract
- This paper deals with queues and insurance risk processes where a generic service time, resp. generic claim, has the form U boolean AND K for some r.v. U with distribution B which is heavy-tailed, say Pareto or Weibull, and a typically large K, say much larger than EU. We study the compound Poisson ruin probability psi(u) or, equivalently, the tail P(W > u) of the M/G/1 steady-state waiting time W. In the first part of the paper, we present numerical values of psi(u) for different values of K by using the classical Siegmund algorithm as well as a more recent algorithm designed for heavy-tailed claims/service times, and compare the results to different approximations of psi(u) in order to figure out the threshold between the light-tailed regime and the heavy-tailed regime. In the second part, we investigate the asymptotics as K -> infinity of the asymptotic exponential decay rate gamma = gamma((K)) in a more general truncated Levy process setting, and give a discussion of some of the implications for the approximations.
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| 6. |
- Asmussen, S, et al.
(författare)
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Transient properties of many-server queues and related QBDs
- 2004
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Ingår i: Queueing Systems. - 0257-0130. ; 46:3-4, s. 249-270
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Tidskriftsartikel (refereegranskat)abstract
- The time tau(n) of first passage from queue length x to queue lengthn > x in a many-server queue with both the arrival process and service intensities governed by a finite Markov process is considered. The mean and the Laplace transform are computed as solutions of systems of linear equations coming out by optional stopping of a martingale obtained as a stochastic integral of the exponential Wald martingale for Markov additive processes. Compared to existing techniques for QBD's, the approach has the advantage of being far more efficient for large n.
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| 7. |
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| 8. |
- Rasmus, Sebastian, et al.
(författare)
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Pricing of some exotic options with NIG-Levy input
- 2004
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Ingår i: Computational Science - ICCS 2004. Proceedings Part IV. (Lecture Notes in Computer Science). - Berlin, Heidelberg : Springer Berlin Heidelberg. - 0302-9743 .- 1611-3349. - 9783540221296 ; 3039, s. 795-802
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Konferensbidrag (refereegranskat)abstract
- We study the problem of pricing barrier options and Russian options driven by exponential NIG Levy processes by simulation. Simulating at a discrete grid creates a systematic bias because the minimum and maximum in between grid points is neglected. The proposed solution is to simulate the large jumps only and use a Brownian approximation for the rest combined with explicit formulas for Brownian minima and maxima.
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