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41.
Quantization consists in studying the L
r
-error induced by the approximation of a random vector X by a vector (quantized version) taking a finite number n of values. We investigate this problem for Gaussian random vectors in an infinite dimensional Banach space and in particular, for Gaussian processes. A precise link proved by Fehringer(4) and Dereich et al.
(3) relates lower and upper bounds for small ball probabilities with upper and lower bounds for the quantization error, respectively. We establish a complete relationship by showing that the same holds for the direction from the quantization error to small ball probabilities. This allows us to compute the exact rate of convergence to zero of the minimal L
r
-quantization error from logarithmic small ball asymptotics and vice versa. 相似文献
42.
Stefan Jaschke Claudia Klüppelberg Alexander Lindner 《Journal of multivariate analysis》2004,88(2):252-273
We derive results on the asymptotic behavior of tails and quantiles of quadratic forms of Gaussian vectors. They appear in particular in delta–gamma models in financial risk management approximating portfolio returns. Quantile estimation corresponds to the estimation of the Value-at-Risk, which is a serious problem in high dimension. 相似文献
43.
In this paper we investigate the
probabilistic linear $(n,\delta)$-widths and $p$-average linear
$n$-widths of the Sobolev space $W^r_2$ equipped with the Gaussian
measure $\mu$ in the $L_{\infty}$-norm, and determine the
asymptotic equalities
\begin{eqnarray*}
\lambda_{n,\delta}(W^r_2,\mu,L_{\infty})
&\asymp&\frac{\sqrt{\ln
(n/\delta)}}{n^{r+(s-1)/2}},\\[3pt]
\lambda^{(a)}_n(W^r_2,\mu,L_{\infty})_p &\asymp&\frac{\sqrt{\ln
n}}{n^{r+(s-1)/2}}, \qquad 0 < p < \infty.
\end{eqnarray*} 相似文献
44.
Wensheng Wang 《Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques》2007,43(5):619-631
The almost sure sample function behavior of the vector-valued fractional Brownian sheet is investigated. In particular, the global and the local moduli of continuity of the sample functions are studied. These results give precise information about the continuity and the oscillation behavior of the sample functions. 相似文献
45.
高斯光束照射下的圆盘夫琅禾费衍射 总被引:9,自引:3,他引:6
推导了高斯光束照射圆孔或圆盘的衍射场普遍表达式,计算了半波带数接近于零的情况下上述衍射场的数据,进而分析了圆盘衍射场在艾里斑中增加一个暗环的原因。 相似文献
46.
Nicholas J. Curro Charles P. Slichter 《Journal of magnetic resonance (San Diego, Calif. : 1997)》1998,130(2):186-194
Measurement ofT2G, the Gaussian component of the spin-echo envelope of planar Cu nuclei in high-temperature superconductors, gives important information about the real part of the Cu electron spin susceptibility. In the traditional picture of the planar Cu echo decay, the internuclear coupling is assumed to remain static with respect to spin–lattice relaxation and mutual exchange fluctuations. In some circumstances, however, this assumption breaks down. We calculate the internuclear corrections arising from spin–lattice relaxation to the conventional theory ofT2Gand show thatT2Gcan be easily corrected for these effects. We argue that mutual exchanges due to the perpendicular indirect couplings are suppressed in these materials. For YBa2Cu4O8, we find a correction on the order of 10% inT2Gand using the corrected values we find that the isotope ratio63T2G/65T2Gagrees with theory. 相似文献
47.
采用高斯分解法(GD)对大非线性相移下的Z扫描特性进行了分析,通过对数值算法的优化,将GD推广到对脉冲入射激光下大非线性相移下的Z扫描理论分析.对不同条件下大非线性相移Z扫描曲线峰谷结构的比较,发现在大非线性相移的情况下,Z扫描曲线的峰和谷随透过光阑或入射光强变化表现出某些新的特性.随着透过光阑孔径的增加,Z扫描曲线峰的变化要明显快于谷的变化,而且在谷明显存在的情况下,峰很快消失.采用皮秒脉冲激光下的纯二硫化碳实验对理论结果加以验证,实验结果和理论分析相一致.我们的分析结果对大非线性相移下Z扫描测量有一定的指导性意义,避免在大非线性相移下对Z扫描结果产生错误的分析.
关键词:
大非线性相移
高斯分解法
Z扫描 相似文献
48.
Alternatives based on polynomial expansions of gaussian basis set exponents are introduced and evaluated. The formulas presented here outperform methods based upon the even-tempered formula or combinations of it. They closely match the performance of other methods based upon larger polynomial expansions of the logarithm of the exponents using the same or one less parameter per orbital angular symmetry. 相似文献
49.
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
50.
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