Brownian Motion Introduction - Properties, Probabilities, Covariance, and Stopping Time скачать в хорошем качестве

Brownian Motion Introduction - Properties, Probabilities, Covariance, and Stopping Time

Brownian motion is the seemingly random movement of particles suspended in a fluid (such as water or air) or dispersed in a medium (like gas or liquid). This phenomenon was first observed by the botanist Robert Brown in 1827 when he noticed pollen grains jiggling about under a microscope in water. Mathematically, Brownian motion is described as a stochastic process, meaning it involves randomness or probability. It is often modeled using the Wiener process, a continuous-time stochastic process that exhibits properties similar to those observed in Brownian motion. Brownian motion has significant implications across various scientific fields, including physics, chemistry, biology, and finance. In physics, it provided early evidence for the existence of atoms and molecules, as their collisions with the suspended particles cause the observed motion. In finance, Brownian motion is used to model the random fluctuations of asset prices and is a fundamental concept in the pricing of options and derivatives. #finance #education