还利用少体硬球系统模拟布朗运动。
布朗运动是分数布朗运动的一种特殊情况。
Brownian motion is a special case of fractional Brownian motion.
随机中点偏移法是生成分形布朗运动的重要方法。
The random mid-point displacement method is an important method in the FBM.
内能增加(温度升高)是由于分子的布朗运动产生的。
The increase of internal energy (temperature rise) results from the molecule Brownian Movement.
布朗运动理论是布莱克-舒尔斯期权定价理论的基础。
The theory of Brownian motion is the foundation of the pricing theory of Black Scholes.
这个简单的结果是粒子扩散和布朗运动的算术和代数基础。
This simple result is at the root of the arithmetic and algebra of Brownian motion and particle diffusion.
很明显，可见的布朗运动与不可见的撞击分子的大小有关。
It is apparent that the visible Brownian motion depends on the size of the invisible bombarding molecules.
估计了一般黎曼流形上的布朗运动关于球面击中时的各阶矩。
Estimations of the moments of the hitting time by Brownian motions on general Riemannian manifolds are also obtained.
给出了多重迭代布朗运动关于球面的首中时的分布与末离时的分布。
The distributions of first hitting time and last exit time of a sphere for multiply iterated Brownian motion are presented.
混沌区周期窗口的存在又表明布朗运动是组织结构和高度有序的表现。
In the chaotic area that periodic Windows exist indicates again the Brownian motion has a characteristic of organizational structure and highly regularity.
本文评述了分数布朗运动和反常扩散现象及描写它们的几种数学方式。
The phenomena of fractional Brownian motion and anomalous diffusion and their descriptive ways in the mathematics are reviewed and discussed.
文摘：给出了多重迭代布朗运动关于球面的首中时的分布与末离时的分布。
Abstract: The distributions of first hitting time and last exit time of a sphere for multiply iterated Brownian motion are presented.
如果风险资产的价格服从几何布朗运动，那么资产市场具有两基金分离现象。
If the price of the risky asset follows the geometric Brownian motion, the asset market exhibits the separation of two funds.
结论是这种力是快速涨落力，强梯度场中核自旋的运动仍然是自由布朗运动。
This additional force is a rapidly fluctuating force, the movement of spins is still free Brownian movement.
事实上，分数布朗运动已经被广泛应用于水文学、随机网络、金融等各个领域。
In fact, the fractional Brownian motion has already been successfully applied to hydrology, network traffic analysis, finance as well as various other fields.
利用玩具激光器对薄膜干涉和布朗运动实验进行改进，使实验现象更加明显、直观。
The film interference experiment and the Brownian motion experiment are improved by using toy laser, and the experimental phenomena are more obviously.
同时，由于布朗运动与微分方程有密切的联系，它又成为概率与分析联系的重要渠道。
Meanwhile, because Brownian motion is closely associated with differential equations, it has become an important channel to contact probability with analysis.
分形高斯噪声fgn是分形布朗运动的增量过程，广泛应用于自相似过程的建模分析。
Fractional Gaussian Noise (FGN) is the increment process of fractional Brownian motion, they are widely used in modelling self-similar process.
研究了基于混合分数布朗运动的债券市场上的价格预测、马尔科夫短期利率和套利问题。
In this article, we focus on the prediction for bond price, arbitrage and Markovian short rates in the bond markets based on mixed fractional Brownian motion.
游戏物理引擎通过避免诸如布朗运动这样的东西来缩减仿真，进而最小化仿真的处理复杂性。
Game physics engines scale back the simulation by avoiding such things as Brownian motion, which in turn minimizes the processing complexities of the simulation.
研究了一列分式布朗运动的起伏极限，证明了广义收敛意义下的大数定律和中心极限定理。
In this paper, we investigate the fluctuation limit of a series of fractional Brownian motions, and prove the large number law and the central limit theorem in generalized convergence.
然而在具体应用中，大部分学者直接将标的资产的价格设为几何布朗运动，并未进行深入研究。
Most researchers directly take an assumption that underlying assets price moving mode is Geometric Brownian Motion, don't ever deeply consider whether it is proper.
我们研究股票市场价格时，通常认为股票价格模型服从布朗运动，即对数收益率是正态分布的。
When we study stock market, we usually think that the model of stock price obeys Brownian movement, which log-return characterize normal distribution.
通过引入用于预测普通商品价格的较成熟的几何布朗运动模型建立了燃煤市场的煤价波动模型。
By means of introducing ripe geometrical Brown movement model for common commodity price forecasting a coal price fluctuation model of coal market is established.
讨论了一类随机控制问题，其脉冲消费控制策略受控于一混合过程——几何布朗运动和泊松过程。
The impulse consumption control strategy of the problem is governed by a mixed process-geometrical Brownian motion and a Poisson process.
讨论了一类随机控制问题，其脉冲消费控制策略受控于一混合过程——几何布朗运动和泊松过程。
The impulse consumption control strategy of the problem is governed by a mixed process-geometrical Brownian motion and a Poisson process.
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