#arcsin law #brownian motion #paradox #stochastic The probability of going through a bad patch We’ve heard it: people that invest on the stock market or that gamble in lotteries, casinos, etc usually say “I’m going through a bad patch” (or bad spell). That is, they have … ...
#brownian motion #einstein #stochastic Brown's observations on Brownian motion In 1828, Robert Brown published the manuscript entitled “A brief account of microscopical observations made in the months of June, July and August 1827, on the particles contained in the pollen … ...
#brownian motion #ito #stochastic differential equation #wiener Introduction to stochastic differential equations Stochastic differential equations (SDEs) are basically inhomogenous ordinary differential equations that depend on an external stochastic process. ...
#brownian motion #kolmogorov #simulation #stochastic #wiener Writing bad letters of recommendation: the story of Bachelier and Lévy Take a coin and toss it a number \(N\) of times in a time interval of duration \(T\). Suppose that every time you get head you win \(a\) euros and that you lose the same amount of money when you get … ...
#brownian motion #diffusion #humans Humans are superdiffusive When tea is poured in a cup of hot water, we observe a phenomenon called diffusion: in the end particles of tea spread evenly throughout the mass of water and we enjoy our cup of tea. Diffusion occurs … ...