A low-order mixed finite element method for a class of quasi-Newtonian Stokes flows. Part I: a priori error analysis

[Abstract] We present a mixed finite element method for a class of non-linear Stokes models arising in quasi-Newtonian fluids. Our results include, as a by-product, a new mixed scheme for the linear Stokes equation. The approach is based on the introduction of both the flux and the tensor gradient of the velocity as further unknowns, which yields a twofold saddle point operator equation as the resulting variational formulation. We prove that the continuous and discrete formulations are well posed, and derive the associated a priori error analysis. The corresponding Galerkin scheme is defined by using piecewise constant functions and Raviart–Thomas spaces of lowest order

GARCH and Irregularly Spaced Data

An exact discretization of continuous time stochastic volatility processes observed at irregularly spaced times is used to give insights on how a coherent GARCH model can be specified for such data. The relation of our approach with those in the existing literature is studied

New general integral transform via Atangana–Baleanu derivatives

Abstract The current paper is about the investigation of a new integral transform introduced recently by Jafari. Specifically, we explore the applicability of this integral transform on Atangana–Baleanu derivative and the associated fractional integral. It is shown that by applying specific conditions on this integral transform, other integral transforms are deduced. We provide examples to reinforce the applicability of this new integral transform

Forecasting Daily Variability of the S and P 100 Stock Index using Historical, Realised and Implied Volatility Measurements

The increasing availability of financial market data at intraday frequencies has not only led to the development of improved volatility measurements but has also inspired research into their potential value as an information source for volatility forecasting. In this paper we explore the forecasting value of historical volatility (extracted from daily return series), of implied volatility (extracted from option pricing data) and of realised volatility (computed as the sum of squared high frequency returns within a day). First we consider unobserved components and long memory models for realised volatility which is regarded as an accurate estimator of volatility. The predictive abilities of realised volatility models are compared with those of stochastic volatility models and generalised autoregressive conditional heteroskedasticity models for daily return series. These historical volatility models are extended to include realised and implied volatility measures as explanatory variables for volatility. The main focus is on forecasting the daily variability of the Standard and Poor's 100 stock index series for which trading data (tick by tick) of almost seven years is analysed. The forecast assessment is based on the hypothesis of whether a forecast model is outperformed by alternative models. In particular, we will use superior predictive ability tests to investigate the relative forecast performances of some models. Since volatilities are not observed, realised volatility is taken as a proxy for actual volatility and is used for computing the forecast error. A stationary bootstrap procedure is required for computing the test statistic and its $p$-value. The empirical results show convincingly that realised volatility models produce far more accurate volatility forecasts compared to models based on daily returns. Long memory models seem to provide the most accurate forecasts

AWAKE: A Proton-Driven Plasma Wakefield Acceleration Experiment at CERN

The AWAKE Collaboration has been formed in order to demonstrate proton-driven plasma wakefield acceleration for the first time. This acceleration technique could lead to future colliders of high energy but of a much reduced length when compared to proposed linear accelerators. The CERN SPS proton beam in the CNGS facility will be injected into a 10 m plasma cell where the long proton bunches will be modulated into significantly shorter micro-bunches. These micro-bunches will then initiate a strong wakefield in the plasma with peak fields above 1 GV/m that will be harnessed to accelerate a bunch of electrons from about 20 MeV to the GeV scale within a few meters. The experimental program is based on detailed numerical simulations of beam and plasma interactions. The main accelerator components, the experimental area and infrastructure required as well as the plasma cell and the diagnostic equipment are discussed in detail. First protons to the experiment are expected at the end of 2016 and this will be followed by an initial three-four years experimental program. The experiment will inform future larger-scale tests of proton-driven plasma wakefield acceleration and applications to high energy colliders