Parameter estimation in stochastic differential equations

Financial processes as processes in nature, are subject to stochastic fluctuations. Stochastic differential equations turn out to be an advantageous representation of such noisy, real-world problems, and together with their identification, they play an important role in the sectors of finance, but also in physics and biotechnology. These equations, however, are often hard to represent and to resolve. Thus we express them in a simplified manner of approximation by discretization and additive models based on splines. This defines a trilevel problem consisting of an optimization and a representation problem (portfolio optimization), and a parameter estimation (Weber et al. Financial Regression and Organization. In: Special Issue on Optimization in Finance, DCDIS-B, 2010). Two types of parameters dependency, linear and nonlinear, are considered by constructing a penalized residual sum of squares and investigating the related Tikhonov regularization problem for the first one. In the nonlinear case Gauss–Newton’s method and Levenberg–Marquardt’s method are employed in determining the iteration steps. Both cases are treated using continuous optimization techniques by the elegant framework of conic quadratic programming. These convex problems are well-structured, hence, allowing the use of the efficient interior point methods. Furthermore, we present nonparametric and related methods, and introduce into research done at the moment in our research groups which ends with a conclusion

On the Gerasimov-Drell-Hearn sum rule for the deuteron

The Gerasimov-Drell-Hearn sum rule is evaluated for the deuteron by explicit integration up to 550 MeV including contributions from the photodisintegration channel and from coherent and incoherent single pion production as well. The photodisintegration channel converges fast enough in this energy range and gives a large negative contribution, essentially from the $^1S_0$ resonant state near threshold. Its absolute value is about the same size as the sum of proton and neutron GDH values. It is only partially cancelled by the single pion production contribution. But the incoherent channel has not reached convergence at 550 MeV.Comment: 6 pages latex including 3 postscript figures, talk at the 15th Int. Conf. on Few-Body Problems in Physics, Groningen, Netherlands, 22-26 July 1997. To be published in Nucl. Phys.

1-(Methoxymethyl)pyrene

The title compound, C18H14O, crystallizes with aromatic �–� stacking interactions

Crystal structure of 25,26,27,28-tetrabenzyloxy-5,11,17,23-tert-butylcalix- [4]arene, C72H80O4

C72H80P4, monoclinic, P121/n1 (no. 14), a = 10.3709(3) Å, b = 23.2467(6) Å, c = 25.1444(7) Å, β= 92.660(1)°, V = 6055.5 Å3, Z = 4, R gt(F) = 0.060, wRref(F2) = 0.190, T = 273 K

Reduction of Eu3 + to Eu2 + in Al-Codoped Silica Glasses Fabricated by the Sol-Gel Technique and CO2-Laser Processing

The spectroscopic properties of europium in aluminium codoped silica glasses produced by the sol-gel technique have been studied with respect to the dopant concentrations and the thermal processing applied to the samples. After thermal annealing at temperatures up to 950_°C the bright red fluorescence around 613 nm characteristic for the trivalent europium ions (Eu3 +) has been observed. The lifetime was measured to be 0.1-2.4 ms depending on dopant concentrations and thermal treatment. Subsequent CO2-laser processing in air (short time remelting) gave rise to a bright blue fluorescence consisting of two broad bands, lying around 450 and 490 nm, with their peak position depending on the ratio between the aluminium and europium concentrations. The fluorescence lifetimes were found to be shorter than 1 μ s. This blue fluorescence is attributed to the divalent europium ion (Eu2 +), leading to the conclusion that the CO2-laser processing of europium doped alumina-silica glasses resulted in the reduction of the trivalent to the divalent europium ion. Laser processing could therefore be a valid alternative to conventional thermal annealing for the generation of Eu2 + in alumina-silica glasse