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还利用少体硬球系统模拟布朗运动。Brownian motion is simulated by using hard-ball systems.

经典的B-S模型是建立在布朗运动环境下的。Classical B-S model was established in Brownian motion environment.

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求出了布朗束缚振子的平均第一通过时间。The mean first-passage time of the Brownian bound oscillator is obtained.

分形布朗运动是模拟此类信号的很好的数学模型。Fractional Brownian motion is a convenient model for this kind of process.

一个布朗运动粒子的路径是不规则的，并且常常改变方向。The path of a particle in Brownian motion is erratic and frequently changes direction.

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.

布朗运动是一种重要的随机过程，它的首出时的分布在很多方面有着重要的应用。Its distribution of the first passage time for Brownian motion are used in many subjects.

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同时，天文学家可以寻找时空版的随机布朗运动。At the same time, astronomers can look for the spacetime analogues of random Brownian motion.

研究布朗束缚振子在马尔可夫极限下的统计性质。The Statistical properties of Brownian bound oscillator under the Markovian limit are studied.

咱们每一天都试图领悟一样平常股价波动的布朗运动的一些法则。Every day, we try to discern some kind of order in the Brownian motion of day-to-day stock volatility.

通过蒙特卡罗模拟方法，得到布郎粒子定向梯跳运动曲线。Through the numerical simulation, a direct stepping motion curve of single Brownian particle is obtained.

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.

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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.

所以，研究分数布朗运动环境中的期权定价更具有广泛性和实用性。Therefore, the study of option pricing in fractional Brownian motion environment is much more wide and practical.

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.

空气和水对它们而言跟蜂蜜一样黏稠，布朗运动则让分子的行径全无章法。Air and water feel as thick as molasses, and Brownian motion militates against forcing molecules to move in precise ways.

只要有一架不要求是质量特别好的显微镜，就可以观察布朗运动。The only apparatus necessary for observing Brownian motion is a microscope, which need not even be a particularly good one.

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其中包括有布朗运动，热噪声，信息理论，熵和作者本身对麦克斯韦妖的看法。Topics include Brownian motion, thermal noise, information theory, entropy, and the author's personal view of Maxwell's Demon.

文章论述了分形、分数维的基本概念，以及分数布朗运动的数学模型。The conceptions of fractal, fractal dimension and the mathematical model of fractional Brownian motion are discussed in this paper.

对于单个布朗粒子的情形，我们给出了统一的微扰解析解，它对大、小阻尼情形均适用。For the single Brownian particle case, we give unified perturbative analytic expressions valid for both large and small friction cases.