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Event(s) on February 2006

  • Tuesday, 7th February, 2006

    Title: The Pseudo-Transient Continuation Method for Solving Nonlinear Equations
    Speaker: Professor C. T. Kelley, Department of Mathematics, North Carolina State University, USA
    Time/Place: 11:30  -  12:30
    RRS 905
    Abstract: Pseudo-transient continuation is a method for finding dynamically stable solutions of nonlinear equations. The approach mimics temporal integration, but uses large time steps toward the end of avoiding the cost of a fully timeaccurate simulation. In this talk we will compare pseudo-transient continuation to conventional damped Newton method approaches, discuss convergence results and time step control, and present some examples.

  • Friday, 10th February, 2006

    Title: Error Estimates of Binomial Tree Methods for American Option Pricing
    Speaker: Professor Lishang Jiang, Department of Mathematics, Tongji University, China
    Time/Place: 16:00  -  17:00
    Abstract: In this talk we like to talk about error estimates in C-norm of BTM for American-style options such as vanilla options and jump-diffusion models, which are based on the equivalence theorems between BTM and the explicit finite difference methods in a critical case for free boundary problems,.

  • Tuesday, 21st February, 2006

    Title: Numerical Study of Airflow and Pollutant Transport in Urban Street Canyons
    Speaker: Dr. Chun-Ho Liu, Department of Building and Real Estate, The Hong Kong Polytechnic University
    Time/Place: 11:30  -  12:30
    FSC 1217
    Abstract: Computational fluid dynamic (CFD) techniques, including 3D large-eddy simulation(LES) and 2D − k turbulence model, are used to investigate the characteristic airflow and gaseous pollutant transport in street canyons of different aspect ( b h / , building-height-tostreet-width) ratios in this study. Airflow and pollutant transport for idealized street canyons of aspect ratio 0.5, 1 and 2 at a Reynolds number ( Re ) of 12,000 and a Schmidt number ( Sc ) of 0.72 are considered. When the approaching wind is perpendicular to the street axis, both LES and − k turbulence model calculate a primary recirculation which is confined to the street canyon and is isolated from the free-stream flow. As a result, the pollutant removal is accomplished solely by (vertical) turbulent transport at the roof level. LES calculates that the pollutant removal occurs at the leeward roof level and the retention of pollutant inside the street canyon is more than 95%. The mean-flow properties calculated by the − k turbulence model agree well with the LES outputs, whereas, LES explains the detailed spatio-temporal transport processes by turbulence. Making use of the CFD results, the air exchange (ACH) and pollutant exchange (PCH) rates are calculated by LES and − k turbulence model, in which their difference in ACH rates is less than 20%. Additional CFD results show that buoyancy-driven street-canyon flow markedly changed the characteristic air recirculation in isothermal situations. At sufficiently high temperature difference (between wall surfaces and ambient), the recirculating airflow structure is no longer isolated from the free-stream flow. Subsequently, the vertical mean flow also contributes to the air ventilation and pollutant dilution. The air removal is still dominated by vertical velocity fluctuation but including buoyancy could enlarge the ACH rate by almost a factor of 4 at large temperature difference.

  • Wednesday, 22nd February, 2006

    Title: Nonparametric Transition - Based Tests for Diffusions
    Speaker: Dr. Peng Heng, Department of Operations Research and Financial Engineering, Princeton University, USA
    Time/Place: 14:30  -  15:30
    Abstract: We develop a specification test for the transition density of a discretely-sampled continuous-time diffusion process, based on a comparison of a nonparametric estimate of the transition density or distribution function to their corresponding parametric counterparts assumed by the null hypothesis. Using the closed form expansions for the transition density of Ait-Sahalia (2002) under the null parametric model and the explicit nonparametric estimate of transition density of Fan, Yao and Tong (1996), we are able to consider a direct comparison of the two densities for an arbitrary specification of the null parametric model. Using two different discrepancy measures between the null and alternative transition density and distribution functions, we simultaneously test the model's assumptions on the drift and diffusion functions. Our approach does not impose the assumption that the alternative model is a one-factor diffusion model and allows multi-factor stochastic volatility models or any stationary Markovian processes. We establish the asymptotic null distributions of proposed test statistics and compute their power functions. The finite sample properties are critically investigated via simulation studies and are compared with the test statistic of Hong and Li (2005).



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