查询词典 Wiener process

At this in, we prove theorem of the modulus of continuity of levy under the condition of weighted sum that averagesinterval segments about normal wiener process, discuss that define in chapter 2 under of the Wiener process Be adding the power line to combine under of increase quantity have much small.

在这一章中，我们证明了关于标准Wiener过程的等间距分段加权和的Lévy连续模定理，讨论了在第二章中定义下的Wiener过程在加权线性组合下的增量有多小。

In the first chapter , we consider the law of iterated logarithm with finite partial sum. Under certain condition ,we extend the law of iterated logarithm with finite partial sum for the Wiener process to Gaussian process ; In addition, we apply the law of iterated logarithm of Chung to the finite partial sum condition.

第一章考虑有限项部分和的重对数律，在一定条件下，将 Wiener过程下有限项部分和的重对数律推广到高斯过程中，得到高斯过程下的有限项部分和的重对数律；另外，将Chung氏重对数律进一步推广到有限项部分和的情形下。

It briefly introduces the Wiener Process as a most important class in the random process.

在本章中，简要地介绍了Wiener过程作为随机过程中重要的一类，它与其他学科的密切联系，和关于此过程一些已经取得的重要成果，以及与本论文有关的一些工作。

Chapter four studies the chaotic responses in a system consisting of simple pendulum and harmonic oscillator under bounded noise excitation. Firstly, the Melnikov function of the two-degree-of-freedom system under Hamiltonian perturbation is derived. The essential condition of the autonomous system for the probable onset of chaos is obtained, the Poincare maps of the system under small Hamiltonian perturbation and the effect of increasing perturbation on the Poincare maps are studies. Then for the non-autonomous system under damping and harmonic or bounded noise excitation, the largest Lyapunov exponent and Poincare maps are calculated. From the analysis of the largest Lyapunov exponent, the critical criterion for the onset of chaos, and the conclusion that the threshold of bounded noise amplitude for the onset of chaos in the system increases as the intensity parameter of Wiener process increases are obtained. The result from the analysis of Poincare maps is in agreement with that obtained from the Largest Lyapunov exponent. The effect of varying damping coefficient and intensity parameter of Wiener process is also analyzed.

第四章研究了有界噪声激励下的两自由度单摆—谐振子系统的混沌运动，首先推导了该两自由度系统仅在Hamilton扰动下的Melnikov函数，得到该自治系统可能产生混沌的必要条件；研究了该系统在小的Hamilton扰动和增大摄动情形下的Poincare截面；然后对有阻尼、谐和或有界噪声激励下的非自治系统数值计算了其最大Lyapunov指数和Poincare截面；从Lyapunov指数分析得到了这个两自由度系统产生混沌运动的临界条件及产生混沌的临界激励幅值随Wiener过程强度参数值的增大而增大的结论，Poincare截面分析的结果亦符合Lyapunov指数分析的结论；研究了Wiener过程强度参数、阻尼系数变化对Poincare截面的影响。

In this paper,we mainly make a deep and systematic study of sample path prop-erties for high and infinite dimensional Gaussian processes,especially for high andinfinite dimensional Wiener process in stronger norm-Holder norm than ever(everbefore,there used to be uniform norm and the process was limited to one dimen-sion).We not only deal with all kinds of functional moduli of continuity,but alsoconcern with different forms of functional limit theorems of C-R increments.

本文主要对高维的以至无穷维的Gauss过程、特别是Wiener过程的样本轨道性质在较以往更强的范数—〓范数下作了系统深入的研究（以往通常采用一致范数，过程限于一维），研究的内容不仅包括各种形式的泛函连续模，而且还包括各种形式的C-R增量的泛函极限定理。

In the last years,some new developments were gotten,but they are only for a Wiener process.

最近几年来，这些方面的研究有了一些新的进展，但一直来只限于Wiener过程。

For example, constant modulus of levy and the increments of a Wiener Process all depend on this inequality.

关于Wiener过程增量的尾概率的估计不等式在讨论Wiener过程增量的性质中十分有用，像Levy连续模定理及Wiener过程增量有多大的证明都依赖于这一不等式。

Finally, in the Wiener process of increase the property of the quantity is the foundation that studies a heavy logarithms of the Wiener process.

总之，Wiener过程中的增量的性质是研究Wiener过程重对数率的基础。

In this, the synopsis ground introduced the Wiener process conduct and actions random importance in the process of a type, it and the close contact of other academicses is some to have already obtain with concerning this process of important result, and have relation with this thesis of some works.

在这一章中，简要地介绍了Wiener过程作为随机过程中重要的一类，它与其他学科的密切联系，和关于此过程一些已经取得的重要成果，以及与本论文有关的一些工作。

For example, constant modulus of levy and the increments of a Wiener Process.

关于Wiener过程增量的尾概率的估计不等式在讨论Wiener过程性质中十分有用，像Levy连续模定理及Wiener过程增量有很多的证明都依赖于这一不等式。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。