3,183 research outputs found

    Pathwise optimal transport bounds between a one-dimensional diffusion and its Euler scheme

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    In the present paper, we prove that the Wasserstein distance on the space of continuous sample-paths equipped with the supremum norm between the laws of a uniformly elliptic one-dimensional diffusion process and its Euler discretization with NN steps is smaller than O(N−2/3+Δ)O(N^{-2/3+\varepsilon}) where Δ\varepsilon is an arbitrary positive constant. This rate is intermediate between the strong error estimation in O(N−1/2)O(N^{-1/2}) obtained when coupling the stochastic differential equation and the Euler scheme with the same Brownian motion and the weak error estimation O(N−1)O(N^{-1}) obtained when comparing the expectations of the same function of the diffusion and of the Euler scheme at the terminal time TT. We also check that the supremum over t∈[0,T]t\in[0,T] of the Wasserstein distance on the space of probability measures on the real line between the laws of the diffusion at time tt and the Euler scheme at time tt behaves like O(log⁥(N)N−1)O(\sqrt{\log(N)}N^{-1}).Comment: Published in at http://dx.doi.org/10.1214/13-AAP941 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

    Drift dependence of optimal trade execution strategies under transient price impact

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    We give a complete solution to the problem of minimizing the expected liquidity costs in presence of a general drift when the underlying market impact model has linear transient price impact with exponential resilience. It turns out that this problem is well-posed only if the drift is absolutely continuous. Optimal strategies often do not exist, and when they do, they depend strongly on the derivative of the drift. Our approach uses elements from singular stochastic control, even though the problem is essentially non-Markovian due to the transience of price impact and the lack in Markovian structure of the underlying price process. As a corollary, we give a complete solution to the minimization of a certain cost-risk criterion in our setting

    Hot Zero and Full Power Validation of PHISICS RELAP-5 Coupling

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    PHISICS is a reactor analysis toolkit developed over the last 3 years at the Idaho National Laboratory. It has been coupled with the reactor safety analysis code RELAP5-3D. PHISICS is aimed at providing an optimal trade off between needed computational resources (in the range of 10~100 computer processors) and accuracy. In fact, this range has been identified as the next 5 to 10 years average computational capability available to nuclear reactor design and optimization nuclear reactor cores. Detailed information about the individual modules of PHISICS can be found in [1]. An overview of the modules used in this study is given in the next subsection. Lately, the Idaho National Laboratory gained access plant data for the first cycle of a PWR, including Hot Zero Power (HZP) and Hot Full Power (HFP). This data provides the opportunity to validate the transport solver, the interpolation capability for mixed macro and micro cross section and the criticality search option of the PHISICS pack

    Lymphogranuloma venerum

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    This issue of eMedRef provides information to clinicians on the pathophysiology, diagnosis, and therapeutics of lymphogranuloma venerum

    Geomagnetism and Aeronomy activities in Italy during IGY, 1957/58

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    In 2007 several events were organized to celebrate the fiftieth anniversary of the International Geophysical Year (IGY, 1957-1958). The celebrations will last until 2009 and are taking place within different contexts: the International Polar Year (IPY), the International Heliophysical Year (IHY), the electronic Geophysical Year (eGY) and the International Year of Planet Earth (IYPE). IGY offered a very appropriate and timely occasion to undertake a series of coordinated observations of various geophysical phenomena all over the globe. Italy took part in the broad international effort stimulated by IGY. In fact, Italy participated in observations and studies in many of the proposed scientific areas, in particular Geomagnetism and Aeronomy. The Istituto Nazionale di Geofisica (ING) started the installation of observatories, and updated and ensured continuous recording of geophysical observations. Geomagnetism, ionospheric physics, seismology, and other geophysical disciplines, were advanced. Although much of the work was undertaken in Italy, some attention was also devoted to other areas of the world, in particular Antarctica, where Italy participated in seismological observations. This paper gives a summary of the Geomagnetism and Ionospheric Physics activities within IGY. Furthermore, we highlight the importance of this historical event and its outcomes for the improvement of geophysical observations and the post-IGY growth of scientific investigations in Italy

    Flow Pressure Behavior Downstream of Ski Jumps

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    Ski jump spillways are frequently implemented to dissipate energy from high-speed flows. The general feature of this structure is to transform the spillway flow into a free jet up to a location where the impact of the jet creates a plunge pool, representing an area for potential erosion phenomena. In the present investigation, several tests with di erent ski jump bucket angles are executed numerically by means of the OpenFOAM¼ digital library, taking advantage of the Reynolds-averaged Navier–Stokes equations (RANS) approach. The results are compared to those obtained experimentally by other authors as related to the jet length and shape, obtaining physical insights into the jet characteristics. Particular attention is given to the maximum pressure head at the tailwater. Simple equations are proposed to predict the maximum dynamic pressure head acting on the tailwater, as dependent upon the Froude number, and the maximum pressure head on the bucket. Results of this study provide useful suggestions for the design of ski jump spillways in dam construction

    Geomagnetism and Aeronomy activities in Italy during IGY, 1957/58

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    In 2007 several events were organized to celebrate the fiftieth anniversary of the International Geophysical Year (IGY, 1957-1958). The celebrations will last until 2009 and are taking place within different contexts: the International Polar Year (IPY), the International Heliophysical Year (IHY), the electronic Geophysical Year (eGY) and the International Year of Planet Earth (IYPE). IGY offered a very appropriate and timely occasion to undertake a series of coordinated observations of various geophysical phenomena all over the globe. Italy took part in the broad international effort stimulated by IGY. In fact, Italy participated in observations and studies in many of the proposed scientific areas, in particular Geomagnetism and Aeronomy. The Istituto Nazionale di Geofisica (ING) started the installation of observatories, and updated and ensured continuous recording of geophysical observations. Geomagnetism, ionospheric physics, seismology, and other geophysical disciplines, were advanced. Although much of the work was undertaken in Italy, some attention was also devoted to other areas of the world, in particular Antarctica, where Italy participated in seismological observations. This paper gives a summary of the Geomagnetism and Ionospheric Physics activities within IGY. Furthermore, we highlight the importance of this historical event and its outcomes for the improvement of geophysical observations and the post-IGY growth of scientific investigations in Italy

    Higher current algebras, homotopy Manin triples, and a rectilinear adelic complex

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    The notion of a Manin triple of Lie algebras admits a generalization, to dg Lie algebras, in which various properties are required to hold only up to homotopy. This paper introduces two classes of examples of such homotopy Manin triples. These examples are associated to analogs in complex dimension two of, respectively, the punctured formal 1-disc, and the complex plane with multiple punctures. The dg Lie algebras which appear include certain higher current algebras in the sense of Faonte, Hennion and Kapranov arXiv:1701.01368. We work in a ringed space we call rectilinear space, and one of the tools we introduce is a model of the derived sections of its structure sheaf, whose construction is in the spirit of the adelic complexes for schemes due to Parshin and Beilinson.Comment: 60 page

    Optimal execution strategies in limit order books with general shape functions

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    We consider optimal execution strategies for block market orders placed in a limit order book (LOB). We build on the resilience model proposed by Obizhaeva and Wang (2005) but allow for a general shape of the LOB defined via a given density function. Thus, we can allow for empirically observed LOB shapes and obtain a nonlinear price impact of market orders. We distinguish two possibilities for modeling the resilience of the LOB after a large market order: the exponential recovery of the number of limit orders, i.e., of the volume of the LOB, or the exponential recovery of the bid-ask spread. We consider both of these resilience modes and, in each case, derive explicit optimal execution strategies in discrete time. Applying our results to a block-shaped LOB, we obtain a new closed-form representation for the optimal strategy, which explicitly solves the recursive scheme given in Obizhaeva and Wang (2005). We also provide some evidence for the robustness of optimal strategies with respect to the choice of the shape function and the resilience-type

    Towards non-perturbative BV-theory via derived differential cohesive geometry

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    We propose a global geometric framework which allows one to encode a natural non-perturbative generalisation of usual Batalin-Vilkovisky (BV-)theory. Namely, we construct a concrete model of derived differential cohesive geometry, whose geometric objects are formal derived smooth stacks, i.e. stacks on formal derived smooth manifolds, together with a notion of differential geometry on them. This provides a working language to study generalised geometric spaces that are smooth, infinite-dimensional, higher and derived at the same time. Such a formalism is obtained by combining Schreiber's differential cohesion with the machinery of T\"oen-Vezzosi's homotopical algebraic geometry applied to the theory of derived manifolds of Spivak and Carchedi-Steffens. We investigate two classes of examples of non-perturbative classical BV-theories in the context of derived differential cohesion: scalar field theory and Yang-Mills theory.Comment: 106 pages, 11 figure
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