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61.
Our purpose is to characterize the multiparameter Gaussian processes, that is Gaussian sheets, that are equivalent in law
to the Brownian sheet and to the fractional Brownian sheet. We survey multiparameter analogues of the Hitsuda, Girsanov and
Shepp representations. As an application, we study a special type of stochastic equation with linear noise.
相似文献
62.
Peter Friz Nicolas Victoir 《Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques》2007,43(6):775-785
We study large deviation principles for Gaussian processes lifted to the free nilpotent group of step N. We apply this to a large class of Gaussian processes lifted to geometric rough paths. A large deviation principle for enhanced (fractional) Brownian motion, in Hölder- or modulus topology, appears as special case. 相似文献
63.
64.
Let (E, ¦·¦) be a uniformly convex Banach space with the modulus of uniform convexity of power type. Let be the convolution of the distribution of a random series inE with independent one-dimensional components and an arbitrary probability measure onE. Under some assumptions about the components and the smoothness of the norm we show that there exists a constant such that |{·<t}–{·+r<t}|r
q
, whereq depends on the properties of the norm. We specify it in the case ofL
spaces, >1. 相似文献
65.
Sandro Faetti Leone Fronzoni Paolo Grigolini Vincenzo Palleschi Girolamo Tropiano 《Journal of statistical physics》1988,52(3-4):979-1003
Two models for the Freedericksz transition in a fluctuating magnetic field are considered: one is based on a dichotomic and the other on a nonlinear Gaussian noise. Both noises are characterized by a finite correlation time. It is shown that the linear response assumption leading to the best Fokker-Planck approximation in the dichotomic and nonlinear Gaussian cases can be trusted only up to the order
1 and
0, respectively. The role of the corrections to the linear response approximation is discussed and it is shown how to replace the non-Fokker-Planck terms stemming from these corrections with equivalent terms of standard type. This technique is shown to produce perfect agreement with the exact analytical results (dichotomic noise) and to satisfactorily fit the results of analog simulation (nonlinear Gaussian noise). 相似文献
66.
Sandro Faetti Leone Fronzoni Paolo Grigolini Riccardo Mannella 《Journal of statistical physics》1988,52(3-4):951-978
It is shown that the Fokker-Planck operator can be derived via a projection-perturbation approach, using the repartition of a more detailed operator into a perturbation
1 and an unperturbed part
0. The standard Fokker-Planck structure is recovered at the second order in
1, whereas the perturbation terms of higher order are shown to provoke the breakdown of this structure. To get rid of these higher order terms, a key approximation, local linearization (LL), is made. In general, to evaluate at the second order in
1 the exact expression of the diffusion coefficient which simulates the influence of a Gaussian noise with a finite correlation time, a resummation up to infinite order in must be carried out, leading to what other authors call the best Fokker-Planck approximation (BFPA). It is shown that, due to the role of terms of higher order in
1, the BFPA leads to predictions on the equilibrium distributions that are reliable only up to the first order in t. The LL, on the contrary, in addition to making the influence of terms of higher order in
1 vanish, results in a simple analytical expression for the term of second order that is formally coincident with the complete resummation over all the orders in t provided by the Fox theory. The corresponding diffusion coefficient in turn is shown to lead in the limiting case to exact results for the steady-state distributions. Therefore, over the whole range 0 the LL turns out to be an approximation much more accurate than the global linearization proposed by other authors for the same purpose of making the terms of higher order in
1 vanish. In the short- region the LL leads to results virtually coincident with those of the BFPA. In the large- region the LL is a more accurate approximation than the BFPA itself. These theoretical arguments are supported by the results of both analog and digital simulation. 相似文献
67.
68.
《Surface and interface analysis : SIA》2005,37(7):589-607
The accuracy of quantitative XPS analysis can be improved using predetermined transmission functions. Two different calibration methods are used for estimating the transmission function T(E) of a photoelectron spectrometer, applying a survey spectra approach (SSA) and a quantified peak‐area approach (QPA) to minimize the quantification error. For the SSA method, Au, Ag and Cu spectra measured with the Metrology Spectrometer II have been used. The new QPA method was built up from Au 4f, Au 4d, Au 4p3/2, Ag 3d, Ag 3p3/2, Cu 3p, Cu 2p3/2, Ge 3p and Ge 2p3/2 standard peak areas, applying adequate ionization cross‐sections and mean free path lengths for different pass energies (10 and 50 eV), lens modes (large area, large area XL, small area 150) and x‐ray sources (Al/Mg Twin and Al Mono). In the energy range 200–1500 eV a transmission function T(E) = a0 + b1E (where a0, b1 and b2 are variable parameters) was found to give an appropriate approximation for eight tested spectrometer settings, implementing the largest changes in the case of pass energy variations. Determination and application of the transmission functions were integrated in the XPS analysis software (UNIFIT 2004) and tested by means of an Ni90Cr10 alloy. The results demonstrate the practicability of the SSA and QPA methods, giving decreased errors of <8% in comparison with errors up to 38% obtained using Wagner's sensitivity factors. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
69.
A comparative study for the fitting of X‐ray photoelectron spectra (XPS) using different model functions is presented. Synthetically generated test spectra using Gaussian/Lorentzian convolution and a real measured spectrum are fitted with the three commonly used models: product, sum and Gaussian/Lorentzian convolution functions. In these limited tests, it was found that the sum function is superior to the product function, particularly for low‐noise spectra. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
70.
用密度泛含方法研究了LaC5n(n=-1,0,+1)分子簇的结构和稳定性及振动光谱,对这个六原子体系提出了三种可能构型,点群结构为C2v对称性.第一个构型为La接在弯曲的C5链上,第二个是La通过二个键与C5环相连第三个是La通过一个键与C5环相连;结果表明,第一个构型即当La接在弯曲的C5链上时能量最低.振动光谱分析指出,当n=-1时,第二个构型为局域极小值;当n=+1时,第一个和第二个构型为局域极小值;对n=0,局域极小值没有找到. 相似文献