Smoothness and asymptotic estimates of densities for SDEs with locally smooth coefficients and applications to square root-type diffusions

We study smoothness of densities for the solutions of SDEs whose coefficients are smooth and nondegenerate only on an open domain $D$. We prove that a smooth density exists on $D$ and give upper bounds for this density. Under some additional conditions (mainly dealing with the growth of the coefficients and their derivatives), we formulate upper bounds that are suitable to obtain asymptotic estimates of the density for large values of the state variable ("tail" estimates). These results specify and extend some results by Kusuoka and Stroock [J. Fac. Sci. Univ. Tokyo Sect. IA Math. 32 (1985) 1--76], but our approach is substantially different and based on a technique to estimate the Fourier transform inspired from Fournier [Electron. J. Probab. 13 (2008) 135--156] and Bally [Integration by parts formula for locally smooth laws and applications to equations with jumps I (2007) The Royal Swedish Academy of Sciences]. This study is motivated by existing models for financial securities which rely on SDEs with non-Lipschitz coefficients. Indeed, we apply our results to a square root-type diffusion (CIR or CEV) with coefficients depending on the state variable, that is, a situation where standard techniques for density estimation based on Malliavin calculus do not apply. We establish the existence of a smooth density, for which we give exponential estimates and study the behavior at the origin (the singular point).Comment: Published in at http://dx.doi.org/10.1214/10-AAP717 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Trivariate polynomial approximation on Lissajous curves

We study Lissajous curves in the 3-cube, that generate algebraic cubature formulas on a special family of rank-1 Chebyshev lattices. These formulas are used to construct trivariate hyperinterpolation polynomials via a single 1-d Fast Chebyshev Transform (by the Chebfun package), and to compute discrete extremal sets of Fekete and Leja type for trivariate polynomial interpolation. Applications could arise in the framework of Lissajous sampling for MPI (Magnetic Particle Imaging)

Modeling and Simulation of Nonlinearly Loaded Electromagnetic Systems via Reduced Order Models - A Case Study: Energy Selective Surfaces

L'abstract è presente nell'allegato / the abstract is in the attachmen

Creating personas for political and social consciousness in HCI design

Personas have become an important tool for Human-Computer Interaction professionals. However, they are not immune to limitations and critique, including stereotyping. We suggest that while some of the criticisms to personas are important, the use of personas is open to them in part because of an unquestioned focus on explicating user needs and goals in traditional persona research and creation. This focus, while helping designers, obscures some other potentially relevant aspects. In particular, when the goal of the product or software being designed is associated with social and political goals rather than with bringing a product to the market, it may be relevant to focus personas on political aspirations, social values and the will or capacity of personas to take action. We argue that it is possible when producing personas (and associated scenarios) to partially move away from representing needs and embrace personas which more explicitly represent political or social beliefs and values. We also suggest that a phenomenographic approach to user data analysis is one way to achieve this. We provide empirical evidence for our position from two large-scale European projects, the first one in the area of Social Innovation and the second in the area of eParticipation

Bivariate Lagrange interpolation at the Padua points: the ideal theory approach

Padua points is a family of points on the square $[-1,1]^2$ given by explicit formulas that admits unique Lagrange interpolation by bivariate polynomials. The interpolation polynomials and cubature formulas based on the Padua points are studied from an ideal theoretic point of view, which leads to the discovery of a compact formula for the interpolation polynomials. The $L^p$ convergence of the interpolation polynomials is also studied.Comment: 11 page

Study of new rare event simulation schemes and their application to extreme scenario generation

This is a companion paper based on our previous work on rare event simulation methods. In this paper, we provide an alternative proof for the ergodicity of shaking transformation in the Gaussian case and propose two variants of the existing methods with comparisons of numerical performance. In numerical tests, we also illustrate the idea of extreme scenario generation based on the convergence of marginal distributions of the underlying Markov chains and show the impact of the discretization of continuous time models on rare event probability estimation