The tt-dependence of the pure DVCS cross section at COMPASS

The key reactions to study the Generalised Parton Distributions are Deeply Virtual Compton Scattering (DVCS) and Deeply Virtual Meson Production (DVMP). At COMPASS, these processes are investigated using a high intensity muon beam with a momentum of 160\,GeV/c and a 2.5\,m-long liquid hydrogen target. In order to optimize the selection of exclusive reactions at these energies, the target is surrounded by a new barrel-shaped time-of-flight system to detect the recoiling particles. COMPASS-II covers the up to now unexplored $x_{B}$ domain ranging from 0.01 to 0.15. From the sum of cross sections measured with positive and negative beam polarities, the pure DVCS cross-section and its $t$-dependence have been extracted resulting in a first model-independent determination of the transverse size of the partonic distribution of the nucleon $\sqrt{}= (0.578 \ \pm \ 0.042\ _{- \ 0.018}^{+ \ 0.006})\,\textsf{fm} $at a mean$x_{B}$ value of 0.056.Comment: Conference proceeding to the XXIV International Workshop on Deep-Inelastic Scattering and Related Subject

Proxy simulation schemes using likelihood ratio weighted Monte Carlo for generic robust Monte-Carlo sensitivities and high accuracy drift approximation (with applications to the LIBOR Market Model)

We consider a generic framework for generating likelihood ratio weighted Monte Carlo simulation paths, where we use one simulation scheme K° (proxy scheme) to generate realizations and then reinterpret them as realizations of another scheme K* (target scheme) by adjusting measure (via likelihood ratio) to match the distribution of K° such that E( f(K*) | F_t ) = E( f(K°) w | F_t ). This is done numerically in every time step, on every path. This makes the approach independent of the product (the function f) and even of the model, it only depends on the numerical scheme. The approach is essentially a numerical version of the likelihood ratio method [Broadie & Glasserman, 1996] and Malliavin's Calculus [Fournie et al., 1999; Malliavin, 1997] reconsidered on the level of the discrete numerical simulation scheme. Since the numerical scheme represents a time discrete stochastic process sampled on a discrete probability space the essence of the method may be motivated without a deeper mathematical understanding of the time continuous theory (e.g. Malliavin's Calculus). The framework is completely generic and may be used for high accuracy drift approximations and the robust calculation of partial derivatives of expectations w.r.t. model parameters (i.e. sensitivities, aka. Greeks) by applying finite differences by reevaluating the expectation with a model with shifted parameters. We present numerical results using a Monte-Carlo simulation of the LIBOR Market Model for benchmarking.Monte-Carlo, Likelihood Ratio, Malliavin Calculus, Sensitivities, Greeks

On suboptimal control design for hybrid automata using predictive control techniques

In this paper we propose an on-line design technique for the target control problem, when the system is modelled by hybrid automata. First, we compute off-line the shortest path, which has the minimum discrete cost, from an initial state to the given target set. Next, we derive a controller which successfully drives the system from the initial state to the target set while minimizing a cost function. The model predictive control (MPC) technique is used when the current state is not within a guard set, otherwise the mixed-integer predictive control (MIPC) technique is employed. An on-line, semi-explicit control algorithm is derived by combining the two techniques. Finally, as an application of the proposed control procedure, the high-speed and energy-saving control problem of the CPU processing isconsidered