Brownian motion stochastic process models. There exist both simpler and more complicated stochastic processes which in extreme ("taken to the limit") may describe the Brownian Motion (see random walk and Donsker's theorem). The Roman Lucretius's scientific poem "On the Nature of Things" (c. 60 BC) has a remarkable description of Brownian motion of dust particles in verses 113–140 from Book II. He uses this as a proof of the existence of atoms: "Observe what happens when sunbeams are admitted into a building and shed light on its shadowy places. You will see a multitude of tiny particles mingling in a multitude of
Brownian model of financial markets to the Lebesgue measure. Brownian model of financial markets The Brownian motion models for financial markets are based on the work of Robert C. Merton and Paul A. Samuelson, as extensions to the one-period market models of Harold Markowitz and William F. Sharpe, and are concerned with defining the concepts of financial assets and markets, portfolios, gains and wealth in terms of continuous-time stochastic processes. Under this model, these assets have continuous prices evolving continuously in time and are driven by Brownian motion processes. This model requires an assumption of perfectly divisible assets and a frictionless market (i.e. that no