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

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

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 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

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

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

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. The sharpness and applicability of these results are illustrated by a counterexample proving the nonexistence of a full LDP in the J1 topology, and by an application to a first passage problem

Search for a W ' boson decaying to a muon and a neutrino in pp collisions at √s =7 TeV

This is the Pre-Print version of the Article. The official published version can be accessed from the link below - Copyright @ 2011 ElsevierA new heavy gauge boson, W', decaying to a muon and a neutrino, is searched for in pp collisions at a centre-of-mass of 7 TeV. The data, collected with the CMS detector at the LHC, correspond to an integrated luminosity of 36 inverse picobarns. No significant excess of events above the standard model expectation is found in the transverse mass distribution of the muon-neutrino system. Masses below 1.40 TeV are excluded at the 95% confidence level for a sequential standard-model-like W'. The W' mass lower limit increases to 1.58 TeV when the present analysis is combined with the CMS result for the electron channel.This work is supported by the FMSR (Austria); FNRS and FWO (Belgium); CNPq, CAPES, FAPERJ, and FAPESP (Brazil); MES (Bulgaria); CERN; CAS, MoST, and NSFC (China); COLCIENCIAS (Colombia); MSES (Croatia); RPF (Cyprus); Academy of Sciences and NICPB (Estonia); Academy of Finland, ME, and HIP (Finland); CEA and CNRS/IN2P3 (France); BMBF, DFG, and HGF (Germany); GSRT (Greece); OTKA and NKTH (Hungary); DAE and DST (India); IPM (Iran); SFI (Ireland); INFN (Italy); NRF and WCU (Korea); LAS (Lithuania); CINVESTAV, CONACYT, SEP, and UASLP-FAI (Mexico); PAEC (Pakistan); SCSR (Poland); FCT (Portugal); JINR (Armenia, Belarus, Georgia, Ukraine, Uzbekistan); MST and MAE (Russia); MSTD (Serbia); MICINN and CPAN (Spain); Swiss Funding Agencies (Switzerland); NSC (Taipei); TUBITAK and TAEK (Turkey); STFC (United Kingdom); DOE and NSF (USA)

Measurement of the charge ratio of atmospheric muons with the CMS detector

This is the pre-print version of this Article. The official published version can be accessed from the link below - Copyright @ 2010 ElsevierWe present a measurement of the ratio of positive to negative muon fluxes from cosmic ray interactions in the atmosphere, using data collected by the CMS detector both at ground level and in the underground experimental cavern at the CERN LHC. Muons were detected in the momentum range from 5 GeV/c to 1 TeV/c. The surface flux ratio is measured to be 1.2766 \pm 0.0032(stat.) \pm 0.0032 (syst.), independent of the muon momentum, below 100 GeV/c. This is the most precise measurement to date. At higher momenta the data are consistent with an increase of the charge ratio, in agreement with cosmic ray shower models and compatible with previous measurements by deep-underground experiments

Observation of a new Xi(b) baryon

The first observation of a new b baryon via its strong decay into Xi(b)^- pi^+ (plus charge conjugates) is reported. The measurement uses a data sample of pp collisions at sqrt(s) = 7 TeV collected by the CMS experiment at the LHC, corresponding to an integrated luminosity of 5.3 inverse femtobarns. The known Xi(b)^- baryon is reconstructed via the decay chain Xi(b)^- to J/psi Xi^- to mu^+ mu^- Lambda^0 pi^-, with Lambda^0 to p pi^-. A peak is observed in the distribution of the difference between the mass of the Xi(b)^- pi^+ system and the sum of the masses of the Xi(b)^- and pi^+, with a significance exceeding five standard deviations. The mass difference of the peak is 14.84 +/- 0.74 (stat.) +/- 0.28 (syst.) MeV. The new state most likely corresponds to the J^P=3/2^+ companion of the Xi(b).Comment: Submitted to Physical Review Letter