Its basic property is that Brownian motion W(t) is a normal random variable with an expected value of 0 and a variance of t (time). For any R less than or equal to S, W(t)-W(s) has nothing to do with W(r) and is a normal random variable with a variance of T-S. It can be proved that Brownian motion is a Markov process, a martingale process and an Ito process.
These small particles are surrounded by liquid molecules. Due to the thermal motion of liquid molecules, small particles are collided by liquid molecules from all directions, and Brownian particles are unbalanced and move in the direction of large impulse. Due to this unbalanced collision, the impulse obtained by Brownian particles constantly changes direction.
Extended data
Irregular motion of Brownian particles. The higher the temperature, the more intense Brownian motion. It indirectly shows that the molecules of matter are in eternal irregular motion.
However, Brownian motion is not limited to the above Brownian particles suspended in liquid or gas. All small objects are impacted by molecules in the surrounding medium and will constantly make tiny random vibrations near their equilibrium positions.
For example, the small mirror on the sensitive vibrating mirror and the filament hanging on other instruments will be collided by the surrounding air molecules, resulting in irregular torsion or vibration.