布朗运动的数学描述是一种相对简单的概率计算，不仅在物理和化学中具有重要意义，而且还用于描述其他统计现象。第一个提出布朗运动数学模型的人是Thorvald N. Thiele在1880年出版的关于最小二乘法的论文中。现代模型是Wiener过程，以纪念Norbert Wiener命名，他描述了a的功能。连续时间随机过程。布朗运动被认为是高斯过程和马尔可夫过程，其具有在连续时间内发生的连续路径。因为液体和气体中原子和分子的运动是随机的，随着时间的推移，较大的颗粒将均匀地分散在整个介质中。如果存在两个相邻的物质区域，并且区域A包含两倍于区域B的粒子，则粒子离开区域A进入区域B的概率是粒子离开区域B进入A的概率的两倍。扩散，粒子从较高浓度区域到较低浓度区域的运动可以被认为是布朗运动的宏观示例。影响流体中颗粒运动的任何因素都会影响布朗运动的速率。例如，升高的温度，增加的颗粒数量，小的颗粒尺寸和低的粘度增加了运动速率。大多数布朗运动的例子是运输过程，它们也受到较大电流的影响，但也表现出了pedesis。
The mathematical description of Brownian motion is a relatively simple probability calculation that is not only important in physics and chemistry, but also used to describe other statistical phenomena. The first person to propose a mathematical model of Brownian motion was in the paper on the least squares method published by Thorvald N. Thiele in 1880. The modern model is the Wiener process, commemorating the name of Norbert Wiener, who describes the function of a. Continuous time random process. Brownian motion is considered to be a Gaussian process and a Markov process with continuous paths that occur over continuous time. Because the movement of atoms and molecules in liquids and gases is random, larger particles will be evenly dispersed throughout the medium over time. If there are two adjacent material regions, and region A contains twice as many particles as region B, then the probability of the particles leaving region A entering region B is twice the probability that the particles will enter A from zone B. Diffusion, the movement of particles from a higher concentration region to a lower concentration region can be considered as a macroscopic example of Brownian motion. Any factor that affects the motion of the particles in the fluid affects the rate of Brownian motion. For example, elevated temperatures, increased particle count, small particle size and low viscosity increase the rate of motion. An example of most Brownian motions is the transport process, which is also affected by larger currents, but also shows pedesis.