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Some properties and convergence theorems of the Henstock variational integral for stochastic process with respect to canonical Brownian motion are probed.

讨论了关于布朗运动的随机积分用Henstock变差逼近的方法所定义的积分的一些性质和收敛定理。

The representation of functionals of Brownian motion in terms of stochastic integral with respect to Brownian motion is known as Clark formula.

布朗泛函以布朗运动随机积分来表示是可被称之为克拉克公式。

In Part Ⅰ,using thestrong Markov property and the first passage time between two levelswe consider three classes of stochastic integral functionals.

我们得到了一些有效算法，讨论了它们的极限性质。在这部分工作中，我们不仅推进了Puri，P.S。

The major topics are: Poisson process, renewal process, discrete time and continuous time Markov chains, stationary process, Brown motion and stochastic integral introduction

本课程的主要内容包括泊松过程与更新过程、离散时间与连续时间的马尔可夫链、平稳过程、布朗运动与随机积分初步。

In order to meet the ride comfort of the heavy truck cab when on line-haul, the H2 control algorithm based on the linear matrix inequalities is presented for the active control of a 6 degree-of-freedom half-heavy-truck suspension system model. The road disturbance is integral white-noise stochastic signal.

为了满足长途运输时重型卡车行驶的平顺性要求，利用基于线性矩阵不等式的H2控制算法对驾驶室安装了主动悬置的六自由度1/2重型卡车模型进行振动控制，所采用的路面激励为积分白噪声随机路面激励。

By applying the H〓lder inequality, the Gronwall inequality, the Doob's inequality and the properties of the Ito stochastic integral to the integral form of the test equation, several important inequalities related to the analytical solution are proved, and the local order of the numerical solutions in mean square sense is obtained accordingly.

通过对试验方程的积分形式使用Holder不等式、Gronwall不等式、Doob不等式和Ito随机积分的性质，得出了试验方程解析解满足的几个重要不等式，进而得出了数值方法在均方意义下的局部误差阶。

It was supposed that the dynamic moving process of the stock price and the return was driven by Geometry Brownian Motion and the lognormal distribution respectively. Takinginto account the riskneutral environment, we got a closedform analytical formula for deferred arithmetic asian options by the method of Taylor expansion of the stochastic integral formula within the terminal payoff. Furthermore, with the series definition of the definite integral, we transferred the continuous problem into a discrete one which is simpleenough to figure out. Meanwhile we tested the accuracy of the formula with the Monte Carlo simulation as a benchmark and the result shows that the formula can be utilized to price the related financial derivatives.

在标的价格服从几何布朗运动、收益服从对数正态分布的前提下，通过风险中性定价原理，对到期损益中的随机积分进行任意次Taylor近似，并由级数定义将此连续问题离散化，给出了延期算术平均亚式期权封闭形式的解析定价公式，并与Monte Carlo模拟得到的价格作为标尺对得到的公式进行精确性检验，结果表明，所得公式可以应用到金融实务中对此类衍生品定价中。

New properties and improvements on VSI. Combining the density processof local absolute continuous measure, properties of the martingale space H1 and semi-martingale space, and the closed image theorem of functional analysis (see the proofs ofTheorem 2.4.5 and Theorem 2.4.10), we obtain the general form of Girsanov Theorem forsemi-martingale vector stochastic integral .

特别是利用局部绝对连续测度的密度过程、鞅空间H1与半鞅空间的性质以及泛函分析中的闭图像定理(见定理2.4.5与定理2.4.10的证明)获得了一般形式的半鞅向(来源：Ab6BC论a1文网www.abclunwen.com)量随机积分的Girsa-nov定理，它对于随机分析的理论与随机积分的应用都具有重要价值。

As Legendre integration is one of Gauss integration, it is nature to apply the others Gauss integration into stochastic FEM.

为了减少在多随机变量情况下的该方法的计算量，建立了一种简化算法，推导出利用单随机变量的响应结果构造多随机变量的响应。

Then we give some premiliaries, including stochastic integration for fractional Brownian motion, parameter estimates in the fraction...

第三章是本文的主要部分，给出了分数O-U过程中参数估计的大偏差，并且给出了证明。

In contrast to the ubiquitous rising-sun-with-rays military flag of the Japanese, Chinese banners and ensigns feature a range of designs.

与遍地都是的太阳军旗不同，中国人的旗帜和徽章设计得各式各样。

From their small corner of Feng's Guangzhou headquarters -- a jumble of pink leashes, squeezable rubber steaks, and plastic doggy Santas for Fido's stocking -- Soleil's designers come up with at least five new products a month.

从Feng 设在广州总部的产品展示柜台上可以看到，Soleil的设计师每月至少设计出5件新产品。