Path properties of the solution to the stochastic heat equation with L\'evy noise

We consider sample path properties of the solution to the stochastic heat equation, in $\mathbb{R}^d$ or bounded domains of $\mathbb{R}^d$, driven by a L\'evy space-time white noise. When viewed as a stochastic process in time with values in an infinite-dimensional space, the solution is shown to have a c\`adl\`ag modification in fractional Sobolev spaces of index less than $-\frac d 2$. Concerning the partial regularity of the solution in time or space when the other variable is fixed, we determine critical values for the Blumenthal-Getoor index of the L\'evy noise such that noises with a smaller index entail continuous sample paths, while L\'evy noises with a larger index entail sample paths that are unbounded on any non-empty open subset. Our results apply to additive as well as multiplicative L\'evy noises, and to light- as well as heavy-tailed jumps

Stochastic expansions using continuous dictionaries: L\'{e}vy adaptive regression kernels

This article describes a new class of prior distributions for nonparametric function estimation. The unknown function is modeled as a limit of weighted sums of kernels or generator functions indexed by continuous parameters that control local and global features such as their translation, dilation, modulation and shape. L\'{e}vy random fields and their stochastic integrals are employed to induce prior distributions for the unknown functions or, equivalently, for the number of kernels and for the parameters governing their features. Scaling, shape, and other features of the generating functions are location-specific to allow quite different function properties in different parts of the space, as with wavelet bases and other methods employing overcomplete dictionaries. We provide conditions under which the stochastic expansions converge in specified Besov or Sobolev norms. Under a Gaussian error model, this may be viewed as a sparse regression problem, with regularization induced via the L\'{e}vy random field prior distribution. Posterior inference for the unknown functions is based on a reversible jump Markov chain Monte Carlo algorithm. We compare the L\'{e}vy Adaptive Regression Kernel (LARK) method to wavelet-based methods using some of the standard test functions, and illustrate its flexibility and adaptability in nonstationary applications.Comment: Published in at http://dx.doi.org/10.1214/11-AOS889 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

The "Window Problem" in Studies of Children's Attainments: A Methodological Exploration

Numerous studies of the determinants of children's attainments rely on observations of circumstances and events at age 14 as proxies for information over the entire childhood period. Using 21 years of panel data from the Michigan PSID on 825 children who were 14-16 years old in 1979, we evaluate the effects of using truncated or "window" (e.g., age 14) information in models of the determinants of attainments (e.g., education, nonmarital fertility) of young adults. Correlations between truncated and full-childhood variables are presented, along with 5 tests of the reliability of estimates based on "window" measurements. The tests are designed to evaluate the differential effects of data accuracy, multiple occurrence of events, duration of circumstances, and the timing of events or circumstances during childhood between "window" and full childhood information. We conclude that most of the standard truncated variables serve as weak proxies for multi-year information in such models, and draw the implications of these findings for future data-collection and research.

Charged Higgs Production at Linear Colliders in Large Extra Dimensions

In the Two-Higgs-Doublet Model(2HDM) with large extra dimensions(LED), we study the contributions of virtual Kaluza-Klein(KK) gravitons to 2HDM charged Higgs production, especially in the two important production processes $e^+e^-\to H^+H^-$ and $e^+e^-\to H^-t\bar{b}$, at future linear colliders (LC). We find that KK graviton effects can significantly modify these total cross sections and also their differential cross sections compared to their respective 2HDM values and, therefore, can be used to probe the effective scale $\Lambda_T$ up to several TeV. For example, at $\sqrt{s}=2$ TeV, the cross sections for $e^+e^-\to H^+H^-$ and $e^+e^-\to H^-t\bar{b}$ in the 2HDM are 7.4fb for $m_{H^-}=150$ GeV and 0.003fb for $m_{H^-}=1.1$ TeV and $\tan\beta=40$, while in LED they are 12.1fb and 0.01fb, respectively, for $\Lambda_T=4$ Tev.Comment: 18 pages, 11 figures; a version to appear in PR

Next-to-leading order QCD predictions for pair production of neutral Higgs bosons at the CERN Large Hadron Collider

We present the calculations of the complete NLO inclusive total cross sections for pair production of neutral Higgs bosons through $b\bar b$ annihilation in the minimal supersymmetric standard model at the CERN Large Hadron Collider. In our calculations, we used both the DREG scheme and the DRED scheme and found that the NLO total cross sections in the above two schemes are the same. Our results show that the $b\bar b$-annihilation contributions can exceed ones of $gg$ fusion and $q\bar q$ annihilation for $h^0H^0$, $A^0h^0$ and $A^0H^0$ productions when $\tan\beta$ is large. In the case of $\mu>0$, the NLO corrections enhance the LO total cross sections significantly, which can reach a few tens percent, while for $\mu<0$, the corrections are relatively small, and are negative in most parameter space. Moreover, the NLO QCD corrections can reduce the dependence of the total cross sections on the renormalization/factorization scale, especially for $\mu<0$. We also use the CTEQ6.1 PDF sets to estimate the uncertainty of LO and NLO total cross sections, and find that the uncertainty arising from the choice of PDFs increases with the increasing $m_{A^0}$.Comment: 43 pages, 16 figures, minor changes, some references added, a version to appear in PR

Forecasting U.S. Trade in Services

This paper provides a set of forecasts of United States international trade in services, both at the aggregate level and for four subcategories. These sectors are: travel, which is mostly tourist expenditures; passenger fares, which is mostly passenger air transportation; transportation, other than passenger transportation; and other private services, including education, financial services, insurance, telecommunications, and business, professional and technical services. A forecasting model is constructed and estimated, based on conventional economic forces of supply and demand, dependent on cost variables and income variables as well as relative prices. For forecasting purposes, these variables are taken from the Michigan Quarterly Econometric Model of the U.S. Economy, a macroeconomic forecasting model with forecasts provided regularly by the University of Michigan Research Seminar in Quantitative Economics. The equations of the services trade model are reported and discussed, and the performance of the estimated equations is evaluated. The quarterly forecast paths are provided for both aggregate and sectoral services trade, including exports and imports, through the end of 2001. Results indicate that imports will continue to rise over the forecast period, while exports, after remaining nearly stationary for several quarters in some sectors in 1999, will resume their rise thereafter. This forecasting work is to be continued, and it is suggested, in addition, that future research would be useful to explore the determinants of the production and sales of foreign services affiliates of U.S. parent companies.Services, International Trade

Next-to-leading order QCD predictions for graviton and photon associated production in the Large Extra Dimensions model at the LHC

We present the calculations of the complete next-to-leading order(NLO) QCD corrections to the inclusive total cross sections for the Kaluza-Klein(KK) graviton and photon associated production process $pp \to \gamma G_{KK} + X$ in the large extra dimensions(LED) model at the LHC. We show that the NLO QCD corrections in general enhance the total cross sections and reduce the dependence of the total cross sections on the factorization and renormalization scales. When jet veto is considered, the NLO corrections reduce the total cross sections. We also calculate some important differential cross sections for this process at NLO: the missing transverse momentum distribution, the transverse momentum distribution and the pseudorapidity distribution of photon.Comment: 28 pages, 14 figures; minor changes, version published in Phys.Rev.