Geometric Brownian motion by a different Brownian Motion—the model is called a stochastic volatility model. Geometric Brownian motion A geometric Brownian motion (GBM) (also known as exponential Brownian motion) is a continuous-time stochastic process in which the logarithm of the randomly varying quantity follows a Brownian motion (also called a Wiener process) with drift. It is an important example of stochastic processes satisfying a stochastic differential equation (SDE); in particular, it is used in mathematical finance to model stock prices in the Black–Scholes model. A stochastic process "S" is said to follow a GBM if it satisfies the following stochastic differential equation (SDE):
Brownian ratchet Brownian ratchet In the philosophy of thermal and statistical physics, the Brownian ratchet or Feynman-Smoluchowski ratchet is a thought experiment about an apparent perpetual motion machine first analysed in 1912 by Polish physicist Marian Smoluchowski and popularised by American Nobel laureate physicist Richard Feynman in a physics lecture at the California Institute of Technology on May 11, 1962, during his Messenger Lectures series The Character of Physical Law in Cornell University in 1964 and in his text "The Feynman Lectures on Physics" as an illustration of the laws of thermodynamics. The simple machine, consisting of a tiny paddle wheel and