Lyapunov conditions for differentiability of Markov chain expectations: The absolutely continuous case

We consider a family of Markov chains whose transition dynamics are affected by model parameters. Understanding the parametric dependence of (complex) performance measures of such Markov chains is often of significant interest. The derivatives of the performance measures w.r.t. the parameters play important roles, for example, in numerical optimization of the performance measures, and quantification of the uncertainties in the performance measures when there are uncertainties in the parameters from the statistical estimation procedures. In this paper, we establish conditions that guarantee the differentiability of various types of intractable performance measures---such as the stationary and random horizon discounted performance measures---of general state space Markov chains and provide probabilistic representations for the derivatives

Space-filling design for nonlinear models

Performing a computer experiment can be viewed as observing a mapping between the model parameters and the corresponding model outputs predicted by the computer model. In view of this, experimental design for computer experiments can be thought of as devising a reliable procedure for finding configurations of design points in the parameter space so that their images represent the manifold parametrized by such a mapping (i.e., computer experiments). Traditional space-filling designs aim to achieve this goal by filling the parameter space with design points that are as "uniform" as possible in the parameter space. However, the resulting design points may be non-uniform in the model output space and hence fail to provide a reliable representation of the manifold, becoming highly inefficient or even misleading in case the computer experiments are non-linear. In this paper, we propose an iterative algorithm that fills in the model output manifold uniformly---rather than the parameter space uniformly---so that one could obtain a reliable understanding of the model behaviors with the minimal number of design points

Sample Path Large Deviations for Heavy-Tailed Lévy Processes and Random Walks

Let $X$ be a L\'evy process with regularly varying L\'evy measure $\nu$. We obtain sample-path large deviations of scaled processes $\bar X_n(t) \triangleq X(nt)/n$ and obtain a similar result for random walks. Our results yield detailed asymptotic estimates in scenarios where multiple big jumps in the increment are required to make a rare event happen. In addition, we investigate connections with the classical large-deviations framework. In that setting, we show that a weak large deviations principle (with logarithmic speed) holds, but a full large-deviations principle does not hold

Entangled Light in Moving Frames

We calculate the entanglement between a pair of polarization-entangled photon beams as a function of the reference frame, in a fully relativistic framework. We find the transformation law for helicity basis states and show that, while it is frequency independent, a Lorentz transformation on a momentum-helicity eigenstate produces a momentum-dependent phase. This phase leads to changes in the reduced polarization density matrix, such that entanglement is either decreased or increased, depending on the boost direction, the rapidity, and the spread of the beam.Comment: 4 pages and 3 figures. Minor corrections, footnote on optimal basis state

Sample-path large deviations for Lévy processes and random walks with Weibull increments

We study sample-path large deviations for Lévy processes and random walks with heavy-tailed jump-size distributions that are of Weibull type. Our main results include an extended form of an LDP (large deviations principle) in the J1 topology, and a full LDP in the M′1 topology. The rate function can be represented as the solution of a quasi-variational problem. The sharpness and applicability of these results are illustrated by a counterexample proving non-existence of a full LDP in the J1 topology, and an application to the buildup of a large queue length in a queue with multiple servers

Efficient rare-event simulation for multiple jump events in regularly varying random walks and compound Poisson processes

We propose a class of strongly efficient rare-event simulation estimators for random walks and compound Poisson processes with a regularly varying increment/jump-size distribution in a general large deviations regime. Our estimator is based on an importance sampling strategy that hinges on a recently established heavy-tailed sample-path large deviations result. The new estimators are straightforward to implement and can be used to systematically evaluate the probability of a wide range of rare events with bounded relative error. They are “universal” in the sense that a single importance sampling scheme applies to a very general class of rare events that arise in heavy-tailed systems. In particular, our estimators can deal with rare events that are caused by multiple big jumps (therefore, beyond the usual principle of a single big jump) as well as multidimensional processes such as the buffer content process of a queueing network. We illustrate the versatility of our approach with several applications that arise in the context of mathematical finance, actuarial science, and queueing theory

Queue length asymptotics for the multiple-server queue with heavy-tailed Weibull service times

We study the occurrence of large queue lengths in the GI / GI / d queue with heavy-tailed Weibull-type service times. Our analysis hinges on a recently developed sample path large-deviations principle for Lévy processes and random walks, following a continuous mapping approach. Also, we identify and solve a key variational problem which provides physical insight into the way a large queue length occurs. In contrast to the regularly varying case, we observe several subtle features such as a non-trivial trade-off between the number of big jobs and their sizes and a surprising asymmetric structure in asymptotic job sizes leading to congestion

Bhabha Scattering with Radiated Gravitons at Linear Colliders

We study the process e+- e- -> e+- e- +- missing energy at a high-energy e+- e- collider, where the missing energy arises from the radiation of Kaluza-Klein gravitons in a model with large extra dimensions. It is shown that at a high-energy linear collider, this process can not only confirm the signature of such theories but can also sometimes be comparable in effectiveness to the commonly discussed channel e+- e- -> gamma +- missing energy, especially for a large number of extra dimensions and with polarized beams. We also suggest some ways of distinguishing the signals of a graviton tower from other types of new physics signals by combining data on our suggested channel with those on the photon-graviton channel.Comment: 16 pages, LaTex, 8 figures embedded, typos, report no and references correcte

Effect of soil particle size on the electrochemical corrosion behavior of pipeline steel in saline solution

In this study, by using a standard quartz replace of sandy soil particles, the effect of soil particle size (0.1…0.25 mm, 0.6…1.0 mm) on the electrochemical corrosion behavior of X70 pipeline steel in sandy soil corrosive environment simulated by 3.5 wt.% sodium chloride (NaCl) was investigated through polarization curve and electrochemical impedance spectroscopy (EIS) technology. The results indicated that the polarization resistance of X70 steel decreased with a decreasing particle size. For all polarization curves the right shift of cathodic branch with a decreasing particle size is observed. The corrosion of X70 steel is controlled by the cathode process diffusion and oxygen reduction at the metalenvironment interface, the intensity of which increases with the decreasing particle size.З допомогою методів потенціодинамічних поляризаційних кривих та електрохімічної імпедансної спектроскопії (EIS) досліджено корозійну поведінку трубопровідної сталі Х70 у ґрунтовому середовищі, яке змодельовано розчином 3,5 wt.% NaCl з частинками кварцового піску різного розміру (0,1…0,25 і 0,6…1,0 mm). Встановлено, що швидкість корозії сталі зростає зі зменшенням розміру частинок ґрунту, про що свідчить зниження її поляризаційного опору, а також зсув катодних гілок поляризаційних кривих вправо. Зроблено висновок, що в цьому випадку корозію сталі контролює катодний процес відновлення кисню на межі поділу метал–середовище, інтенсивність якого зростає зі зменшенням розміру частинок ґрунту.С помощью методов потенциодинамических поляризационных кривых и электрохимической импедансной спектроскопии (EIS) исследовано коррозионное поведение трубопроводной стали Х70 в почвенной среде, которую моделировали раствором 3,5 wt.% NaCl с частицами кварцевого песка разного размера (0,1…0,25 и 0,6...1,0 mm). Установлено, что скорость коррозии стали растет с уменьшением размера частиц почвы, о чем свидетельствует снижение ее поляризационного сопротивления, а также сдвиг катодных ветвей поляризационных кривых вправо. Сделан вывод, что в данном случае коррозию стали контролирует катодный процесс возобновления кислорода на грани деления металл–среда, нитенсивность которого растет с уменьшением размера частиц почвы

Unparticle physics and lepton flavor violating radion decays in the Randall-Sundrum scenario

We predict the branching ratios of the lepton flavor violating radion decays r -> e^{\pm} \mu^{\pm}, r -> e^{\pm} \tau^{\pm} and r ->\mu^{\pm} \tau^{\pm} in the framework of the Randall-Sundrum scenario that the lepton flavor violation is carried by the scalar unparticle mediation. We observe that their BRs are strongly sensitive to the unparticle scaling dimension and, for its small values, the branching ratios can reach to the values of the order of 10^{-8}, for the heavy lepton flavor case.Comment: 21 pages, 11 Figures, 1 Tabl