Causal cascade in the stock market from the ``infrared'' to the ``ultraviolet''

Modelling accurately financial price variations is an essential step underlying portfolio allocation optimization, derivative pricing and hedging, fund management and trading. The observed complex price fluctuations guide and constraint our theoretical understanding of agent interactions and of the organization of the market. The gaussian paradigm of independent normally distributed price increments has long been known to be incorrect with many attempts to improve it. Econometric nonlinear autoregressive models with conditional heteroskedasticity (ARCH) and their generalizations capture only imperfectly the volatility correlations and the fat tails of the probability distribution function (pdf) of price variations. Moreover, as far as changes in time scales are concerned, the so-called ``aggregation'' properties of these models are not easy to control. More recently, the leptokurticity of the full pdf was described by a truncated ``additive'' L\'evy flight model (TLF). Alternatively, Ghashghaie et al. proposed an analogy between price dynamics and hydrodynamic turbulence. In this letter, we use wavelets to decompose the volatility of intraday (S&P500) return data across scales. We show that when investigating two-points correlation functions of the volatility logarithms across different time scales, one reveals the existence of a causal information cascade from large scales (i.e. small frequencies, hence to vocable ``infrared'') to fine scales (``ultraviolet''). We quantify and visualize the information flux across scales. We provide a possible interpretation of our findings in terms of market dynamics.Comment: 9 pages, 3 figure

A multifractal random walk

We introduce a class of multifractal processes, referred to as Multifractal Random Walks (MRWs). To our knowledge, it is the first multifractal processes with continuous dilation invariance properties and stationary increments. MRWs are very attractive alternative processes to classical cascade-like multifractal models since they do not involve any particular scale ratio. The MRWs are indexed by few parameters that are shown to control in a very direct way the multifractal spectrum and the correlation structure of the increments. We briefly explain how, in the same way, one can build stationary multifractal processes or positive random measures.Comment: 5 pages, 4 figures, uses RevTe

The impact of new neutrino DIS and Drell-Yan data on large-x parton distributions

New data sets have recently become available for neutrino and antineutrino deep inelastic scattering on nuclear targets and for inclusive dimuon production in pp pd interactions. These data sets are sensitive to different combinations of parton distribution functions in the large-x region and, therefore, provide different constraints when incorporated into global parton distribution function fits. We compare and contrast the effects of these new data on parton distribution fits, with special emphasis on the effects at large x. The effects of the use of nuclear targets in the neutrino and antineutrino data sets are also investigated.Comment: 24 pages, 13 figure

Polarized Parton Densities

In this talk we summarize main results of a recent determination of the polarized deeply inelastic parton distributions to NLO from the world data. In the analysis the LO and NLO parton densities and their $1\sigma$ statistical errors were derived and parameterized. The strong coupling constant $\alpha_s(M_Z^2)$ is determined $\alpha_s(M_Z^2) = 0.113 \pm 0.004 {\rm (stat.)} \pm~0.004 {\rm (fac.)} +0.008/-0.005 {\rm (ren.)}$ Comparisons of the low moments of the parton densities with recent lattice results are given. A detailed error-analysis of the gluon density is performed.Comment: 3 pages LATEX, 1 style file, 1 eps file, to appear in the Proceedings of PANIC '02, Osaka, Ocrober 200

EPS09 - Nuclear PDFs and Their Uncertainties at NLO

In this talk, we present our recent next-to-leading order (NLO) nuclear parton distribution functions (nPDFs), which we call EPS09. As an extension to earlier NLO analyses, we supplement the deep inelastic scattering and Drell-Yan dilepton data by inclusive midrapidity pion measurements from RHIC in order to reduce the otherwize large freedom in the nuclear gluon densities. Our Hessian-type error analysis leading to a collection of nPDF error sets, is the first of its kind among the nPDF analyses.Comment: 4 pages, 4 figures - To appear in the conference proceedings for Quark Matter 2009, March 30 - April 4, Knoxville, Tennesse

Nucleus polarizability contribution to the hydrogen-deuterium isotope shift

The correction to the hydrogen-deuterium isotope shift due to the proton and deuteron polarizability is evaluated on the basis of modern experimental data on the structure functions of inelastic lepton-nucleus scattering. The numerical value of this contribution is equal 63\pm 12 Hz.Comment: 5 page

Relating high-energy lepton-hadron, proton-nucleus and nucleus-nucleus collisions through geometric scaling

A characteristic feature of small-x lepton-proton data from HERA is geometric scaling -- the fact that over a wide range of x and Q^2 all data can be described by a single variable $Q^2/Q_{sat}^2(x)$, with all x-dependence encoded in the so-called saturation momentum $Q_{sat}(x)$. Here, we observe that the same scaling ansatz accounts for nuclear photoabsorption cross sections and favors the nuclear dependence $Q_{sat,A}^2\propto A^{\alpha}Q_{sat}^2$, $\alpha \simeq 4/9$. We then make the empirical finding that the same A-dependence accounts for the centrality evolution of the multiplicities measured in Au+Au collisions at RHIC. It also allows to parametrize the high-p_t particle suppression in d+Au collisions at forward rapidities. If these geometric scaling properties have a common dynamical origin, then this A-dependence of $Q_{sat,A}^2$ should emerge as a consequence of the underlying dynamical model.Comment: 4 pages, 3 postscript figure

Nuclear parton distributions at next to leading order

We perform a next to leading order QCD global analysis of nuclear deep inelastic scattering and Drell-Yan data using the convolution approach to parameterize nuclear parton densities. We find both a significant improvement in the agreement with data compared to previous extractions, and substantial differences in the scale dependence of nuclear effects compared to leading order analyses.Comment: 9 pages, 10 figure

Resummed QCD Power Corrections to Nuclear Shadowing

We calculate and resum a perturbative expansion of nuclear enhanced power corrections to the structure functions measured in deeply inelastic scattering of leptons on a nuclear target. Our results for the Bjorken $x$-, $Q^2$- and $A$-dependence of nuclear shadowing in $F_2^A(x,Q^2)$ and the nuclear modifications to $F_L^A(x,Q^2)$, obtained in terms of the QCD factorization approach, are consistent with the existing data. We demonstrate that the low-$Q^2$ behavior of these data and the measured large longitudinal structure function point to a critical role for the power corrections when compared to other theoretical approaches.Comment: 4 pages, 3 figures, uses RevTeX 4. As published in Phys.Rev.Let